aww.. waw ur situation sounds just like mine, except i never got the chance to live with my bf... and he still hasnt ever came back to me.. = (
but all i would say is that, this is hard, to give him a chance or not... well u should think about all what he did to hurt u, and now when she probably isnt good enough for him anymore he came back to u. u should ask him y does he wanna be with u again? and y he left u for someone else so easily....?
and because i feel that some guys can be extreme selfish jerks.. not caring about their girls feelings, i would say let him be. because he may have came back, but y? and y couldnt he just stick with u and try to help the falling relationship instead of leaving u and then getting with another woman. and now lets say u do give him a chance, u will have to remember he walked out on u and replaced u with someone else. he's an a**hole... if u really feel that u can handle him knowing he was with someone else and then ditched her or whatever the case may be, then talk to him and figure it out, but dont fall for any traps... it is a sticky situation, and u gotta think this time for urself, its not about what u feel, its about what u deserve.... so talk to ur bf, see what he says if he has points to be given another chance then maybe u should, but if he doesnt have any good reasons for all that pain he gave u, then screw him... now u gotta decide and see what ur inner gut tells u... would it be right for me to be with him even after he left me like that and moved on so quick and came back to me, or he was just too messed up and doesnt desereve another chance.....
and yea after my ex left me, i went into this semi depression, and still have thoughts of him feeling a bit nostalgic, but i think if i was talking to him or keeping in touch, my hurt feelings will always remain, and i would always have things to say, because he hurt me... but as time is going on i am more controlling of myself and my feelings.. and i see things more clearly and on how much of a loser he is... it is really really hard to let go, but once u do, u see reality better...
u gotta decide for urself, u can either get back with him and have trust issues extra problems cuz u may say yea i forgive u but inside deep down u may feel a bit nervous or something... and if u let go, ull always wonder and feel like u need him.. but trust me there r better and more fish in the sea.. (in my opinion dont go back to him) but all is ur choice.
good luck.. time will heal it all.