  We present a systematic approach to determine all relativistic phases up to
$\mathcal{O}(c^{-2})$ in light-pulse atom interferometers in weakly curved
spacetime that are based on elastic scattering, namely Bragg diffraction and
Bloch oscillations. Our analysis is derived from first principles using the
parameterized post-Newtonian formalism. In the treatment developed here, we
derive algebraic expressions for relativistic phases for arbitrary
interferometer geometries in an automated manner. As case studies, we consider
symmetric and antisymmetric Ramsey-Bord\'e interferometers, as well as a
symmetric double diffraction interferometer with baseline lengths of 10 m and
100 m. We compare our results to previous calculations conducted for a
Mach-Zehnder interferometer.
