  We demonstrate, using $T=0$ first principles total energy calculations, that
observed pressure-driven anomalies in the entire 122-pnictides family
($A$Fe$_2$As$_2$; $A$ = alkali earth element Ca, Sr, Ba) can be understood as
consequences of Lifshitz transitions (LTs) \cite{Lifshitz60}. Our results for
energy band dispersions and spectra, lattice parameters, enthalpies, magnetism,
and elastic constants over a wide range of hydrostatic pressure provide a
coherent understanding of multiple transitions in these compounds, namely,
enthalpic, magnetic and tetragonal (T) - collapsed tetragonal (cT) transitions.
In particular, the T-cT transition and anomalies in lattice parameters and
elastic properties, observed at finite temperatures, are interpreted as arising
from proximity to $T=0$ Lifshitz transitions, wherein pressure causes
non-trivial changes in the Fermi surface topology in these materials.
