  We study the effects of the Lifshitz transition from closed to open Fermi
surface in dirty topological insulators with the nematic superconductivity near
the critical temperature. We solve linearized Gor'kov equations and find that
the nematic superconductor with an open Fermi surface has a lower critical
temperature and more susceptible to the disorder than the superconductor with
the closed Fermi surface. We propose that correspondence between the critical
temperature and stability against the disorder is the general feature of the
superconductivity. We investigate the effects of the Lifshitz transition on the
competition between superconducting phases in a topological insulator. Open
Fermi surface is beneficial for the nematic order parameter $\Delta_4$ in
competition with orbital-triplet $\Delta_2$ and disfavors nematic state over
the s-wave order parameter. We study Meissner currents in both clean and dirty
limits. We found that transition from closed to open Fermi surface increases
anisotropy of Meissner currents. Finite disorder suppresses superconducting
density stronger than critical temperature. We compare our results with the
existing experimental data.
