In my opinion this is not a matter of amount of overlap. Actually, if you overlap two photos more than 80% you will likely start to see things worsening fast. So rather than amount of overlap, it is a matter of amount of images overlapping.
The circles are called "moiré" and they are a consequence of interference between the two spatial frequencies of the two overlapping images. This moiré will become less noticeable when other paterns superimpose in the same place as more photos are overlapping.
It is somehow like when a few rain drops start falling on water and wave circles are clearly visible, but once the rain becomes heavier, the circles get less noticeable.
Regards