What happens to the wave function of the electrons moving around the loop in exercise 1 (or to the interference pattern if we shoot electrons at a point on the loop in opposite directions on the loop and measure their interference when they cross again) as we undo the figure-eight into a circle in the same plane?

Data From Exercise 1:-

Consider a figure-eight loop made of conductor, mostly in a single plane (with just enough nonplanarity for the loop to not cross itself, but to slightly avoid it), and a constant magnetic field perpendicular to this plane. Do we have an Aharonov-Bohm phase for the electrons in the conducting loop?