Merging separate paths in Illustrator
I have several circles that are set at type none color and 0.01 black stroke. They're all currently in paths (except two I made into compound paths). I want to know how to remove the stroke from the areas where the shapes overlap.
Here is an image:
I want it to look like what's on the right.
What I've done so far: I can get somewhere if I select the two hollow circles which are currently 4 separate paths and make them into a compound path on exclude, but it still looks like the image on the left. I tried removing the anchors, but that does something completely different since those two circles are then broken up into a total of 7 pieces at the intersection points.
If the lower arcs are closed you can Select all the shapes, go to Pathfinder (Window -> Pathfinder) and choose Unite function
Two upper circles are compound path
Select the shapes and click-drag with the Shape Builder Tool to easily combine areas.
Note: That last click-drag I performed isn't really needed :)