While you may have a nice round, over the back "on the bit" trot. And you can have the same canter, sometimes the transition does go to Africa to visit what it's like to be a Giraffe.
What I found best is to keep a constiant contact, light seat (not driving into canter, I want up and under into canter) and then I ask for the transition, if it's not great, I halt, rein back, and ask for trot again, prepare, and then ask for canter again, repeating this transition until we have improvement. Don't over do it, as the horse may become fatigued or sore as they're not used to it.
Also if the horse is anticipating the canter - mix it up, walk more, circles, rein change etc.
So basically do 1000 transitions from trot to canter (or walk to canter if he can do it) and if it's not great, rein back in a straight line for 5 or so steps (this "forces" the horse to naturally come up over his back and use the correct muscles, basically every time you rein back your resetting his muscle memory to be like that so he likes it as is comfortable and will encourage it in the transition!)
Firstly, there is on the bit-a mental state, and round-a physical state. The outside rein controls the 'roundness' you are looking for, and it it used when the outside front leg is on the ground. To ensure he is 'on the bit', a steady contact, where you can feel both sides of the mouth, is required-and the correct neck muscles are shown. Using this, the aids: round, flex and lighten are used into the transition.