Like the guide says, the key is to make sure all transparent content renders from back to front, relative to the camera. The glitches happen when something transparent renders before something that appears behind it, since the transparent parts still fill in the depth buffer, and prevent anything behind it from rendering.
The solution is to use either Z elevation or Z order, or the 'Camera distance' draw order, to ensure the render order is back to front. It looks like you're using meshes and some fairly complicated logic in this example, which makes it harder to figure out. I'd advise to start simple, get it working with that, and then build up from there.