There are many theories regarding the process of the transition/edge change, including a couple of new ones that I believe are grossly effective, but astoundingly difficult to learn. Regardless of where you fall in the spectrum of slalom theory, it is important to understand a few basic principles with respect to the edge change.
1) The edge change is not a change in direction. This is one has been discussed for years, but is still one of the most important ideas. You must maintain your cross-course direction through the edge change.
2) You must have balance on your feet to accomplish the athletic and dynamic movements of the edge change.
3) You must keep your upper body strong and not allow it to be pulled inbound toward the boat. The ski must move out through the transition whilst the upper body stays at least still if not even stronger against the boat than in the approach to the wakes.
4) The transition must start as you approach the middle of the wakes (or bottom of the swing as I often call it). This is not to stay that you will complete the edge change at the center of the wakes, but at least begin the movement.
5) In order to begin the transition at the appropriate time as outlined above, your edge change must be the final and most powerful part of the acceleration phase (also known as “the pull”). The pictures below are a basic example of my edge change and even though it is not one of the best in the sport (in fact it is something I have been working on daily even since these pictures a month ago). Take note of the attempt to keep the ski moving and the power maintained through the edge change. This allows you to keep your direction and approach the turn with ample space, time, and speed to make a controlled and efficient turn.
The main thing I would change about the edge change in this sequence would be to keep my outside shoulder (the right one) a little lower through and after the edge change and drive the reaching arm further in front in order to keep everything moving out more.
