Well, Itachi and Minato are really good at staying calm and analizing the situation to make good tactics, Nagato is just lucky to have Rinnegan so he doesn't even really need to think hard to be strong. Rinnegan is instant-owerful for whoever has it. The fight would be Nagato doing crazy shit most likely, and Itachi whiping out Susano'o first thing from realizing who he's up against. Minato would be analizing both figuring who would be better to take out first.
So honestly, Nagato is going to throw around Shinra Tensei's and summonings like it's nobodies business until either Itachi sneak attacks with Totsuka's sword(like in the manga) or Minato finds an opening and instantly hits Nagato with Rasengan keeping his awareness of Itachi obviously. I think Nagato would actually be the first to die because he'd be spamming shit like he always does and Minato and Itachi would more than likely take him out first keeping aware of each other. But Itachi could get caught by Bansho Tenin and be ****ed. But if it comes down to Itachi vs Minato in the end, Minato is too tricky with Flying Thunder God for Itachi to land a killing blow. Plus Minato's foot speed is comparable to Raikage's, so Sharingan even has a hard time keeping up with Minato's foot speed.(not Flying Thunder God)
Minato wins.
