  The Sagnac time delay and the corresponding Sagnac phase shift, for
relativistic matter and electromagnetic beams counter-propagating in a rotating
interferometer, are deduced on the ground of relativistic kinematics. This
purely kinematical approach allows to explain the ''universality'' of the
effect, namely the fact that the Sagnac time difference does not depend on the
physical nature of the interfering beams. The only prime requirement is that
the counter-propagating beams have the same velocity with respect to any
Einstein synchronized local co-moving inertial frame.
