Kayty makes some good points. When making walk - trot - canter transitions, make sure he is staying balanced in all three gaits, don't canter if he is running in the trot. Never sacrifice the quality of the gaits just to "get something", chances are if you teach him to do something wrong just to "get it", its going to become habit and he'll always do it wrong.
A good exercise for walk - canter transitions is to work on a 20m diameter circle in the walk (after warming up - of course) and then turn onto an 8-10m volte (aka small circle) in the walk. Immediately when you return ot your 20m circle line, ask for the canter. Don't lean forward, don't wiggle around or fling the reins at him, just bring your outside leg back and ask - he should just go. If he doesn't, then teach him what you mean. Just go forward, balanced and make it into the canter. Repeat until he gets it.