Crossing over is used commonly while skating to gain power whether you are going forwards or backwards. In addition, either way they both have the same concept.
When crossing over its depends which leg is crossing the other. For example, if you were to have your right leg cross over your left you will need to lean towards the left side. This technique is moderately difficult but could easily be learned. So when you're crossing over to your left you must bring your right leg as high as possible and cross over your left. However, in this motion you must try to get your right foot as far away from the left to get a deep and powerful cross over.
This is an example of me crossing over in the middle of the motion.