  This paper aims to discuss two issues that can have a significant impact on
the foundations of the theory of gravitation:
  (1). The existence of relativity of space-time geometry with respect to the
properties of used reference frame, which is a manifestation of the long-known
fact of relativity of geometry of space and time with respect to properties of
measuring instruments (Henri Poincare).
  (2). Lack of invariance of Einstein's equations with respect to the geodetic
transformations preserving unchanged the equations of motion of test particles.
Because of this, the physically equivalent states are described, generally
speaking, by means of different solutions of these equations. In other words,
there is no one-to-one correspondence between the solutions of these equations
and the set of admissible physical states
