Here’s a simple animation I created using a technique that I have used for years with video and AfterEffects projects – two swirling objects that pass both in front and behind each other. Essentially, you duplicate the object in back, move it to the front, and trim off a piece where the middle object needs to look like it’s in front, and the cycle the visibility of the front object.
This can also be used, for example, when making a moon orbit a planet, passing behind and in front. With the orbiting moon, adjust the size of the moon from front to back and you can fiddle with the velocity curves to add a touch of drama.