How do you know when the relationship is over?

I’ve been with my boyfriend for 3 years. There’s been a lot of cheating and lies and drinking and disrespect on his part. I’ve become someone I don’t recognize and I’m constantly wondering if he’s truly who I want to be with. He has been showing me that he will change and is changing to become a better person. Our relationship has been decent lately but we fight a lot because of me and the feelings I hold towards him. I can tell he’s upset cause he’s trying to change and be better but no matter what he does, I’m just angry and have a lot of hatred built up in my heart for everything that he has done to me in the past. The most recent was in May. We got into a fight and angrily broke up with each other for the night, which happens often when we’d fight, and he went and slept with someone else that night. Only reason why I ever found out was because she tested positive for chlamydia and got ahold of his sister then came clean to me. He says that he was trying to find a way to tell me but didn’t want to ruin how good we were doing. I can’t trust him to go to the bar, I can’t trust him to hangout with people unless I’m there, I absolutely cannot trust him to stay in a different town and it sucks. I want to whole heartedly give him my trust but he’s ruined it so many times. Like I said, lately I’ve been the problem and just constantly angry. When things are good between us, it’s AMAZING. But when it’s bad, its so so bad. I just don’t know what to do and would appreciate any advice.

UPDATE:

Yesterday was my first day at work (mind you I was afraid to get a job because I was worried he’d just go out and drink and worry about what he does when he drinks). I’m a nurse and I work 12’s. Sure shit around noon he ends up in a different town with some buddies so I was like cool whatever you’re only 40 minutes away, even though you promised me you wouldn’t do this. Texted him and asked what time he was gonna be home and what we should do for dinner and he said “I’m not coming home”. So after 4 years, I can happily say that was my last straw. I applied for my own apartment, broke up with him and am goi g to work on becoming the best me possible. I was okay last night but when I woke up for work this morning and currently pretty sad...but time heals all wounds. Here’s to the start of a new chapter.