I don't like to be asked permission as such but I do like it if a potential new girlfriend introduces herself to me as a friend. I like to be kept in the loop as to what's going on, one step at a time. It's much easier to keep my emotions in check that way and to keep on top of any issues that are bothering me. I think if I were to find out that there was a relationship between one of my partners and someone else that was well underway that I knew nothing about I would consider it cheating.
Everything will be ok in the end. If it's not ok it's not the end.