While doing a left hand reverse saw, start to bring the devilstick toward the center of your body. When the devilstick is rolling over the right handstick bring your left arm around to place the left handstick on the same side the right handstick is. Roll the devilstick over the left handstick and bring your right arm over the devilstick to be in the position to do a right hand forward side saw. The whole time the hands are changing position the devilstick is moving from one side to the other. Practice doing the side to side saw spinning the devilstick in both directions.
Going from a reverse side saw (ie. left hand reverse), to doing a side to side saw transition to the forward side saw (ie. right hand forward) is much easier than going from the forward side saw, to side to side saw transition, to the reverse side saw. Be sure to practice both of these transitions, they are both used for other tricks.
Here are a few variations of the side to side saw.
Shortened side to side saw:
Side to side saw with backside rollovers:
Side to side saw with backside rollovers shown from side angle:
Side to side saw with reverse backside rollovers:
Side to side saw with reverse backside rollovers shown from side angle: