I know it's been long since this happened and all, but I just wanted to share my thoughts. So in chapter 84 when Levi chooses Armin instead of Erwin I wanted to point out something. Levi had more than one reason to make his final decision, but I've noticed that he had made his mind completely and even punched Eren before Mikasa attacked him. I'd say he wasn't even being rational and he didn't even think twice about giving the injection to Erwin.
Desperate and alone, Levi acts impulsively and he's convinced that they can't make it without Erwin.
But when Hanji appears look at his expression
It's like life comes back to his eyes. And he charges a bit his behaviour after seeing her and finding out she's alive
Here when she speaks we can see thoughtful Levi, he isn't giving the injection to Erwin immediately like he was about to do before but, why?
My thoughts are these. Besides Erwin being "drunk" with desire to fulfill his dream leading him to lose his primal selfless goal, and besides Levi feeling empathy on Armin and his friends, I can see Levi finding potential in Hanji as the new leader and inspiration of the corps. Realising he's not alone, that he hasn't lost(from my perspective) the most important person in his life, calls back his senses and he doesn't act desperately anymore becouse he isn't terrified of being alone anymore. It seems like when he thinks Hanji didn't make it he doesn't care about anything anymore, he just acts selfishly and won't listen to anyone's opinion, similar to Mikasa's attitude when she thought she lost Eren. But when he finds out she's okay then he goes back to his normal self. He can think more clearly of what's better, even if the price to pay is really high. Levi said before that "humanity can never defeat titans without Erwin's strength" but I think he sees in Hanji someone who can not replace but take the place of Erwin as the leader and inspiration of humanity.