  From the viewpoint of gauge gravitational theories, the path dependent
gravitational phase factors define the Lorentz transformations between the
local inertial coordinate systems of different positions. With this point we
show that the spectral shifts in the curved spacetime, such as the
gravitational and cosmological redshifts, can be understood as Doppler shifts.
All these shifts are interpreted in a unified way as being originated from the
relative motion of the free falling observers instantaneously static with the
wave source and the receiver respectively. The gravitational phase factor of
quantum systems in the curved spacetime is also discussed.
