  As shown by the development of Special Relativity the simultaneity concept
should be related to that of reference frame. Poincare' proposed to define the
simultaneity of two events by means of light signals following what is nowadays
known as the Einstein simultaneity convention. The need of a simultaneity
definition is present also in general relativity and in curved spacetimes in
order to provide the observers with a coordinate time.
  It is recognized that the old Einstein simultaneity convention is nothing but
a connection on a suitable trivial bundle that defines the reference frame.
Unfortunately, it has a non vanishing holonomy in curved and even in flat
spacetimes a fact that makes it almost useless. We point out the advantage of
local simultaneity conventions showing that they are represented by local
simultaneity connections. Among them there is one, uniquely determined by the
reference frame, which is particularly well-behaved globally.
