One:
Hard Sell
The moment Neal takes that first breath and Peter sees those ridiculous blues eyes pop open is the same moment that Peter realizes just how badly he wants to kiss him. He thinks that it's purely out of the fact that he's ecstatic that the kid's alive, because in that moment, when he laid hands on him and his chest wasn't moving, he thought he would never again see those eyes and that megawatt smile. In that moment he lost all faith in any higher power.
He wouldn't be able to live with himself knowing that Neal was gone because he gave Peter the oxygen over himself and that it was his fault for not forcing it on him. It's Peter's job to protect Neal not the other way around.
God help him if that doesn't make him love him more, but he's awake and smiling, and Peter can't help but smile back. He wants to scoop him up, hold him tight, and tell him how wonderful, brilliant, kind and amazing he his and kiss him again and again.
He would have if, also in that moment, Jones hadn't rushed in followed by, what feels like, every agent in the New York White Collar Division So he just holds him down with a gentle hand on his chest and tells him to breath and hopes no one notices when his hand lingers just a little to long just to feel his heart beating.
Two:
Vital Signs
Peter is furious and terrified, which seems to be the two most common feelings when it comes to Neal Caffery. He's furious that Neal could be so careless and irresponsible and at his total disregard of the fact that there are consequences for his actions, as well as terrified that there's nothing he can do to stop him from going back to prison.
However, as soon as the words You're the only person in my life that I trust come out of his mouth and he gives Peter that look like a child that's broken a window, it all melts away and the only thing left is compassion. Peter runs his fingers through his curls and fights every nerve, muscle and bone in his body not to pull Neal's face in close to his own and kiss it all better.
As much as he hates it he knows has to do something that could yield his own set of severe consequences but he would do anything to not have to see that look on Neal's face ever again.
Three:
Out of the Box
Because you're the only one that could change my mind. Peter can't believe he's just heard those words from Caffery's mouth. He's so close to losing him forever and he tells him he could change his mind. He sees that Neal has tears on his face and he's pretty sure the tears are for him. That alone gives Peter the hope to think he might have a chance.
In that split second before he answers, Did I? a thousand ways to stop him race through his mind and several of them involve some theatrical moment of persuasive kissing. Neal doesn't answer, he just gives him a look and exhales like he spitting out a yes that he can't quite voice. Peter thinks he's done it, that Caffery is gonna stay with him, but when looks at Kate he knows it was no all along.
So he watches him walk towards the plane, towards the new life he's been chasing all year and just when he thinks the kid's going to be gone for good he turns back to him and hope springs eternal. Neal says his name and it rolls off his lips like he confessing something and Peter waits for the longest few seconds of his life to hear the rest. He's sure that Neal is going to give him some speech about how sorry he is and how their time together meant the world to him. Peter thinks this is his chance for that one kiss that will change his mind, but he doesn't get to and he doesn't hear it, he doesn't even have a chance to register what happened before his arms are around Neal and pieces of the plane are falling around them.