  We focus on the Sagnac effect for light beams in order to evaluate if the
higher order relativistic corrections of kinematic origin could be relevant for
actual terrestrial experiments. Moreover, we discuss to what extent the analogy
with the Aharonov-Bohm effect holds true in a fully relativistic framework. We
show that the analogy with the Aharonov-Bohm is not true in general, but is
recovered in a suitable low order approximation, and that even though the
Sagnac effect is influenced by both the position of the interferometer in the
rotating frame and its extension, these effects are negligible for current
terrestrial experiments.
