Search Results: taking ex back

My ex broke up with me on 06/18/17, 3 weeks after we had taken a vacation to Punta Cana to celebrate our 2 yr anniversary. That summer I was a mess and beg him to stayed together but by mid Aug, I was done and cut connections with him. Little after I hear he is dating another girl and that he isn't doing well. Around Nov, he wants to be friends and starts texting me and talking to me and than completely cuts me off when I confront him about his girlfriend who he kept denying he had. This obviously hurt me I tried to get in contact but I realized he had change his number. Fast forward to 05/21/18 (2 days after what would've been our 3rd year). He calls me on the morning tells me that he wants to talk and be friends. So I decided to meet with him and hear him out to see where things are going. Once again I get wrapped up in his words, he tells me that he broke up with the girl he was dating than because she didn't understand him and that he was still in love with me and that he wanted to see where things could go. Obviously me still very much in love with him gives him a chance but I didn't want to make anything official since I wasn't sure how things were really going because he was leaving to Greece in June and wasn't going to get back until Aug. Well what I expected happened, things were great until a week within in his trip where he just stopped replying to my messages and told me that he didn't want to be in contact anymore. So once again he just completely took me out of his life. I needed him to sign my dogs adoption papers because I was traveling abroad and taking my dog with me, so I contacted him when he got back from Greece (he bought me a dog). After that we saw each other a couple of times and hooked up, I told him I couldn't keep doing this because I wanted to date him. He said that's not what he wanted and completely ignore me, all he said is that he was in contact with his ex. Yesterday he calls me after 2 months, to say sorry & that he can't cut me off.

Long story short.
We dated for 5 years and they cheated on me (secret affair for 6 months).
We broke up because they said they felt like they didn't love me anymore and they got with the other person.
We ended up hooking up 3 months into their relationship and they broke up (i didn't feel bad since I was just taking back what was mine).
They stayed single for a year and we got back together.
They went long distance for grad school and ended up cheating (2 months) with another classmate.
We broke up but they never got together.

It's been 2 years and they are claiming that they'll wait for me.
They had some hook ups early on and tried dating but said they wanted no one else.
I still have some feelings and it really looks like they've changed and will stay committed.
My ex is by no means desperate, there are always people hitting on them... I'm amazed they've waited so long even though I promised them nothing.