A good change should be clean, with the front & hind legs changing in the same step. It must also be straight, with no swinging. It should give the impression of going uphill, with the hind legs coming well under the body. The speed & rhythm should remain the same before & after the change.
“The flying change of lead is a fresh canter depart inside the canter” Nuno Oliveira.
The following notes are from personal training experience & research, with references in italics…
The criteria that must be reached before teaching changes
The canter must be established, with a very clear three-beat, & moment of suspension.
The horse must be relaxed, loose & supple.
The hind feet should follow in the same line as the front feet.
The rider should be able to give & retake the reins with the horse remaining in self-carriage & balance.
ADVANCED IN TRAINING:
The horse must be sensitive & obedient to light & subtle aids.
Whilst remaining relaxed, the horse must be able to strike off on either leg anywhere in the arena.
The simple change of leg exercises must be secure.
How advanced in training the horse must be is a *controversial point – some trainers use the lack of balance of the horse to help teach the change, & use the horses natural inclination to change legs to stay in balance. Other trainers want the horses far more advanced, able to counter canter a 10m circle & work in true collection, & taught the changes purely off the correct aids & timing. The latter is the more classically correct.