Help me out guys?

So my boyfriend and I have recently been fighting a lot over something that’s bothering me. I saw him texting another girl asking if they should go out for coffee. I personally don’t mind my boyfriend having friends but this was a girl he didn’t know. A couple days later I asked him ab it if he did and he denied it even when I gave him multiple chances to tell the truth. I told him that I saw the messages and it did upset me that he tried to meet another girl behind my back and then lied about it. But we talked it out and he apologized and said he was wrong. A week after he said the same thing to the same girl and I was so angry that he did it again. And when I asked him he lied AGAIN. He’s never lied to me before and I was really taken aback by it. I told him that I have no problems about him having friends or talking with them but that he should be open and honest about it and not hide it. Because of this I’m always worried that he might meet someone else or flirt with someone else. What can I do? I want to leave but I also want to stay with him but it’s tiring to fight ab and to always worry. We’ve been together for 2 and a half years.
Help me out guys?
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