Given the thickness(es) of the circles and the cutout shapes and the tightness of the build, I believe I would (Smart Guides being your friends, telling you when you are within snapping distance):
1) Create the three full circles with the desired thickness(es, they look a bit different),
2) Create a stroked rectangle with the height of the gap in the innermost circle and align it vertically with the innermost circle, if it covers more then the desired gap then ShiftClickDrag it horizontally so that it no longer does;
3) Copy the rectangle twice and give the two copies the desired heights of the gaps of the outer circles, then lock them and lock the outer circles;
4) Do what Ton said;
5) Lock the innermost set and unlock the middle set and repeat;
6) Lock the middle set and unlock the otermost set and repeat.
There are other ways for 4) such as Ctrl/Cmd+A (hold Ctrl or Cmd and press A) to select the unlocked circle and the unlocked rectangle, then Pathfinder>Minus front for outlined circle, but they are no easier than the ones Ton suggested.