Do overlapping relationships work?

my ex left me and went back to his ex of three years.. he didn't admit it to me for months I had to find out for myself by doing some digging and he would still deny it. I don't understand why. If you love someone why not claim her why not just tell me the truth. It went as far as her getting on a phone and saying they got back together and the next day him calling me telling me she's just a girl he's dated for a month.. my question is do these type of relationships work? They were together for 3 years before me and him were together.
Do overlapping relationships work?
Post Opinion