There's nothing wrong with arguing in a relationship, its common, not everyone will agree on all the same things. however, look at the things you are arguing about. You said you both fight about the small things; honestly I've learned that somethings you just have to let go. Don't let your emotion run high on such a small thing like who's turn it is to throw out the trash etc.. some things can be avoided. Relationships can be hard, and you may not always see eye to eye, but try not to blame each other during these fight, instead express your feelings, and find constructive ways to solve the issues. But remember pick your battles. If you guys both care about each other, you guys will make it work. You just have to learn and understand your partner and their difference and have constructive arguments that better the relationship, not ruin it.