As an observer, you cannot make any measurement in the interval between A and B that can tell the inertial and sagnac observers apart. As the observers travel along an almost identical path (A to B) their clocks must tick at the same rate. And yet one of the observers must measure the speed of light as c (according to relativity) and the other must measure it as c+v or c-v (sagnac effect).

Now relativity argues that if you reference the motion of the sagnac observer to a point in space 1 billion light years away (centre of circle) then everything’s OK, and there’s lots of maths to explain this.
But why should one observer experience changes that make the speed of light vary by v (which can be a very large value), and the other doesn’t. The paths and motions of the observers are indistinguishable by measurement in the interval A to B.

The explanation given by relativity is nonsense.