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.

Answer

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

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Attribution
Source : Link , Question Author : user2899444 , Answer Author : Ilan

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