Ok so let me start off saying I personally believe Uchiha Itachi will win this 3 way fight. So lets very briefly look at what each of the three have:
Minato: Speed is his specialty in this fight and he is also extremely intellegent however Strength and stamina are huge drawbacks for minato. especially strength
Nagato: Stamina and Pure strength are both definitely in his favor
however he lacks in speed and intellegence greatly
Itachi: He is the most Intellegent of the 3. He has a lot of power great at all three types of jutsu. However, itachi lacks in the stamina department which is a drawback.
I saw some people saying nagato can use the paths and fight alongside them. That is incorrect. Nagato had to use the rods and stay stationary to use the paths. However, nagato doesnt need paths for he himself can use ALL the paths abilities at a level which is out of this world compared to the 6 paths. Anyways, Nagato lacks in speed and intellegence (dont claim nagato is smart lmao. the number of mistakes he made in both jiraya's fight and against naruto were unconcievable lol. he is definitely not the sharpest knife in the uzumaki clan.) Ok so speed is his downfall.... We have minato who is way too fast for nagato and we have itachi who can one hit nagato with an amaterasu (yes nagato will die from it. Nagato DID die from it when itachi used amaterasu agaisnt him. However, Nagato was an edo tensei so he was able to shinra tensei it after itachi had told his entire story lmao. And even after he shinra the amaterasu away he STILL had to regenerate from the attack) so nagato isnt living after being hit from amaterasu. Totsuka blade will also hit nagato. Remember Kabuto stated, "nagato does not have the mobility to fight itachi". So lets just assume he doesnt have the mobility to fight minato too lol. Chibaku tensei is actually an easy evasion for both itachi and minato. minato just teleports away. Done. And itachi will use his yasaka magatama spam (we have seen both itachi and madara be capable of using 5 or more magatama's at the same time.) and no the magatama will not need chakra because it is a weapon of the susanoo. He is using chakra to use the susanoo but not it's weaponry...... unfortunately although i personally love nagato (2nd fav char) i believe he will be the first to die or possibly with a lot of luck the second to die. although he has stamina he will not be able to utelize it in a battle like this
Minato: minato is fast and by the time nagato is dead i would like to guess both itachi and minato will have the same amount of chakra left. the question remains who took more damage during the fight and what the situation is. Personally, i believe minato will make a mistake while fighting nagato. Minato is a close ranged fighter. Itachi and nagato are awesome fighters at every range. Minato will either try to attack itachi close range. and be susceptible to Tsukuyomi (if he looks itachi in the eye. And lets all be honest here and not be fanboys. We ALL saw him look tobi dead straight into the eyes even though he had JUST STATED that tobi is Uchiha Madara....... (yes i know tobi isnt uchiha madara.) So Minato is most likely making the same mistake. If he looked "Uchiha Madara" in the eye then i assure you he will look itachi in the eye. Lets say he didnt look itachi in the eye. He will either get hit by amaterasu "not looking itachi in the eye means you have no idea when ur being hit by amaterasu" or he will be hit by the sword of totsuka "he wont see it coming. and if it even scratches minato while minato is close range its "gg" for minato. Also minato has another downfall. Itachi knows all of minatos abilities lol. Itachi was in the anbu as an anbu captain and i assure u that he studied everything about the past hokage's techniques (which is what all the top notch anbu do. remember how 2 of the anbu had the hirashin no jutsu technique and wanted to give it to tsunade to transport to the 5 kage fight?" While minato died when itachi was 5. Knowledge is an important factor in a fight like this. Lets say minato attacked nagato. jesus the number of threats are endless. Freakin bazookas, Summons, shinra tensei, bansho, soul steal techniques. Attacking nagato is a scary thought for minato lol. it is also a scary thought for minato to engage in close range combat with nagato while itachi is "left out" one blast of amaterasu will set both of them on fire. Minato unfortunately lacks in the strength department. As long as itachi has susanoo up and nagato has his summons to protect him minato isnt doing much at all...... 1 mistake "such as getting hit by shinra tensei" will make minato the first victim of the battle. "lets be honest here..... minato has no idea what the hell the rinnegan abilities are. while itachi has an idea due to the uchiha tablet which most likely gives some info such as linked vision ect." The only reason i see minato dying second is because itachi will take out nagato first with one of his high speed long range attacks. Minato isnt getting past a susanoo "sorry guys he just wont. especially if it has the yata mirror attached to it." he wont be expecting the totsuka sword and for heavens sake minato will have no clue what it is when he sees it "lmao orochimaru had been searching for it HIS ENTIRE LIFE and had no idea he was BEING HIT BY IT until he was being sucked in lol" that surprise will be minato's demise. Not to mention the almighty Koto-Amatsukami that itachi has as a secret weapon.....
Itachi: alright the final combatent. Itachi is pretty much a hybrid of nagato and minato. Think about it. He is fast. but not as fast as minato. and he is strong. But not as strong as nagato. So he is right in the middle lol. he is like one of those race car games where you have 3 cars to choose from. 1 that is fast but has no acceleration. 1 that has high acceleration and no speed. and the third which is not as fast and not as high acceleration as the other 2 but is completely equal and right in between. So itachi is right in between. Once he uses susanoo he isnt being touched honestly "dont tell me he cant keep it for a long time. HE WAS ON HIS DEATHBED WHEN HE USED IT AGAINST SASUKE AND HE KILLED OROCHIMARU AND COMPLETELY DRAINED SASUKE OF EVERYTHING HE HAD WHILE IN IT. A healthy itachi will be able to maintain susanoo for a long ass time. Like right now in edo tensei. An edo tensei does not have unlimited stamina FYI. this was exhibited with Muu. Itachi has been using susanoo for how many chapters now? So itachi will most likely take nagato out with an amaterasu. Nagato does shinra itachi will just use amaterasu again..... its really a lose lose situation for nagato unfortunately. cause itachi can also just totsuka sword him. Minato on the other hand is pretty damn fast. if itachi does totsuka sword nagato then minato will know to keep his distance. im pretty sure minato will try to attack the susanoo at some point and find himself hitting the yata mirror. That will most likely mark his downfall. itachi will either catch him with an amaterasu or the totsuka sword then. In the end with minato itachi can really just koto amatsukami him..... but to be fair and not use the overpowered koto amatsukami do any of u really see minato getting past susanoo?. most people theorize that minato can teleport into it. But you realize that a kunai cant go under the susanoo right? even gaaras sand had to be lightened in order to go under madaras susanoo. and IMO itachis susanoo looks even more dense than madara's susanoo. People say minato will teleport around and outlast it? come on now lol. minato will ALSO lose chakra by teleporting around lol. and also itachi has the sharingan. If killer bee a non sharingan user was capable of finding the weakness of hirashin no jutsu i am 100% sure itachi will find the weakness of it after the 5th time minato uses his teleport to evade an attack LOL. Ok well thats it for me lol. have a good one guys