Why should you pay more attention to your cross-overs to improve your jumps? Let's develop this idea. You would be surprised.
First, what is a cross-over ( forward or backward, it's the same)? We bend the leg ( hip/ knee/ ankle) and then extend it to make a push while the upper body remains solid. So, dynamic core and isotonic muscular contraction (concentric and eccentric) are the prerequisites for a jump.
The torso can also be oriented inside the circle to imitate the preparation position of the jumps.
A cross-over is a way to develop power and range of motion, especially for the ankles. The skating boots are getting stiffer, and the ankle development is often forgotten in the workout program ( stability and full range of motion).