Yes, of course Kat is correct with regard to the fact that a horse 'leads' off at the canter with its outside hind. However, when teaching riders initially in using the forces that the horse provides (ie. the power of the hind end) to assist with the upward transition, I find it easier to get the rider to concentrate on their position at the trot first and use that knowledge to 'feel' and get used to the canter transition.
For the purposes of endurance riding (and although I do heartily recommend basic dressage training for both horse and rider) I try to keep the basic intructions as simple as possible so as to keep the rider/s interested and involved. So it may be that I am condoning a not-so-good way to determine this upward transition, however I must say that it seems to work with novice and/or unschooled (in dressage) riders.
My goal is to get the rider into the habit of asking for the upward transition while they are rising out of the saddle at the trot, so that they (gently) land back into the saddle after the canter stride has commenced from the outside hind. The problem I find with novice or unschooled (in dressage) riders is that they often have difficulty in understanding how to 'feel' an action coming from the hind end of the horse, but that it is much easier for the rider to look and feel for the action coming from the front end of the horse.
Once the transition is being asked for and completed easily by the rider, I then gradually introduce the need to 'feel' the action from the rear.
One thing I am pretty happy about is that this thread has forced me to explain in writing what I have been teaching novice riders for a long time.
The current Endurance World Youth FEI standings make interesting reading for me. Of the 25 top Youth riders, 11 are Aussies. Of that 11, there are 3 who started riding (2 of whom I taught to ride) at Splendacrest. Am I pleased? You betcha!
