I would start with five horizontal guide lines evenly distributed to get the top centers of the five circles at the top. Or you could do ten so you have top and bottom. Start with the smallest circle at the top (at the second guideline), then scale up a copy around the first to match with the first guideline. Copy the third, move it down to third guide line and scale up. You will notice that the third "circle" will not be a circle, and you'll need to adjust the top anchor point down,and possibly the shape of the two paths that make up the top half. Similarly the fourth.
Copy this entire set, rotate 180 and offset to create the other side. At this point you will need to add the master circle that encompasses both and probably adjust further. I would adjust just one side and delete the other copy and recopy the adjusted side to make sure they're identical.
Finally, you'll need to use the scissors and delete to cut the overlapped parts out.