I think Sasuke's left eye has got a lot more to it than just shifting or swapping. Don't forget that Sasuke's left eye is actually the Sharingan which Kaguya possessed, not the Rinnegan (although it is claimed to be the Rinnegan as of now). And THAT Sharingan had the ability of Tsukuyomi. I personally think Sasuke's new power is the practical application of Tsukuyomi within a specified range i.e a certain radius around him. So that basically means Sasuke can do all the magic he wants within the limited distance. He can control space, time and mass which are the main traits of Tsukuyomi as depicted by Itachi. Madara realized that and withdrew from that territory Sasuke controls, yet still Sasuke somehow reached to Kakashi's location very swiftly, which startled Madara and he said: You are "still" very fast Sasuke. However, all the substantial mechanics behind the functioning of his eye are still too early to establish i.e its resemblance to FTG and its teleportation ability. BTW, if it is really the Tsukuyomi application, then Sasuke can manipulate time at his own whim which explains Sasuke's moves. For example shifting his location was space time ability and transporting Naruto to the other side is the manipulation of all the subjects: space, time and mass. The same goes for that stabbing action for Madara.