Here is another free photoshop video tutorial, this tutorial explains how you can create intersecting shapes in just a few easy steps.
Here is the description from WatchandLearnPhotoshop
Ever wanted to link two objects together in Photoshop so that they seem to weave in and out of each other, kind of like the Olympic rings? Well, it’s easier than you might think! In this tutorial, you’ll learn how to create this linking effect in just a couple very easy steps.
Watch the tutorial here

An alternative is to use a mask instead as shown in this tutorial:
http://www.lunacore.com/photoshop/tutorials/tut010.htm
Working with duplicates of shapes works fine too, but it’s not perfect since you also duplicate the anti-aliased edge. Not a severe problem though, but it can be noticeable by people with trained eyes.