Wood pigeon mating alternation

I have witnessed this five times in my garden - three times this weekend. There are two wood pigeons on a fence - pigeons A and B. They bill and coo and canoodle. Then pigeon A mounts B, feathers ruffled, and shakes about. This looks like copulation to me. Then A dismounts B and settles on the fence. Pigeon B then mounts A and repeats the performance, in just the same way. What is going on here? (I have 2 videos of it).