  A common approach to metric-affine, local Poincar\'e, special-relativistic
and Galilei spacetime geometry is developed. Starting from an affine composite
bundle, we introduce local reference frames and their evolution along
worldlines and we study both, absolute and relative simultaneity postulates,
giving rise to alternative concepts of spacetime. In particular, the
construction of the Minkowski metric, and its required invariance, allows
either to reorganize the original affine bundle as a metric-affine geometry
with explicit Lorentz symmetry, or to restrict it to a Poincar\'e geometry,
both of them constituting the background of a wide class of gauge theories of
gravity.
