Moved in, but fighting alot? help!?

ive recently moved in with my BF. We hadn't had the greatest past recor big fights lead 2 break-up n heartache. but we've overcome that and now ive moved in. We dont fight like we used to its alot less and less aggression. However, we're always fighting over little things. I think ive got it worked out. We are both REALLY stubborn people. like neither of us will apologise. and always trying to get our point across. we try talking and just listening to each other to solve it. but he never seems to listen to what i have to say. just what he wants to say is important. dont get me wrong. i do the same but not as strongly. He just s in and doesn't take care of wat i was saying. Now im not the type of person to give up n wil stay angry til he makes it better i cant help it. i try 2 but gets me down. n same 4 him. any advice on wat we could do to make us work together in these situations? i care for him deeply. and i believe goes both ways. fights r healthy just want a way to wrk thru it?