You've probably figured this out by yourself by now, but I'm going to say it anyway.
You could try doing different Background System Boxes, each one for each frame of the animation, give them the Parallax qualifier, put all of them in the same X and Y position, and order them in a way that the first frame is on the front of the other two, the second on the middle and the last one is on the back.
Then you can program events that will happen every X frames (which, I guess, you know how to do, you just need a frame counter and a little bit of logic) that will make a frame visible/invisible, depending on which frame you'll need to be visible at a certain time. You need to make the first one invisible, then the second one invisible, then the two visible again, in this order, to make the animation work as it should. There MIGHT be some easier way of doing this, but that's how I do it anyway.
If you don't understand my explanation for any reason, please say so and I'll try to make it more understandable for you.