I would do lots of transitions. Trot for 5 strides then walk. Then trot for 7 strides then. Walk. Then 3 strides etc to mix it up. Get him to anticipate the walk instead of the canter. Once he is controlled at the trot do the same with trot to canter transitions. Trot poles under saddle or on the lunge can also help strengthen and encourage a nicer trot!
I would say change things up. He is probably anticipating because he gets excited for what's next. Make sure to walk some then do circles at the walk then go to trot. When he tries to canter calmly bring him back to the trot and trot until he starts to relax. Then make circles and do a lot of direction changes. Mostly trot don't even try to canter until he is relaxed at a trot. Then slowly add in some cantering. To help the swapping make sure you are staying balanced and work some on circles. I hope this helps some it is hard when someone doesn't know the horse and exactly what it does but this is what I did with my pony jumper when she used to anticipate everything. Good luck:)
This can be because he's unbalanced so as soon as you manage to get him to trot halfhalt him and make him trot slowly and do it on a small circle and then trot for few steps and go back to walk and try again. Don't let him rush. Take your time and let him understand what u wan of him. Putting some trot poles will help in rhythm and make him focused and thinking forward. But I'd only add poles after I managed to get control of his trot.
Try lunging him before mounting. Work on your horse’s transitions and leads. I suggest spending 10-20 minutes veforr every ride, if possible, or 20 minutes weekly lunging your horse and working on his transitions.