I really don't know the spawning behavior for open water spawners, which is what anthias are. I know from my f/w days and cichlid breeding, the lock jaw activity is common between mated pairs, but I don't know what it means in this case. I don't know if open water spawners actually "pair up". I've also heard the female will swim up towards the surface and release the eggs with the male right behind fertilizing. That sounds like the last pic, but I didn't see any egg/sperm release.
I took those pics in a span of about 1 min. They carried on like that for maybe 1/2 hr, then just went back to their normal swimming around.