  We induce and study a topological dynamical phase transition between two
planar superconducting phases. Using the
  Lindblad equation to account for the interactions of Bogoliubov
quasiparticles among themselves
  and with the fluctuations of the superconducting order parameter, we derive
the relaxation dynamics
  of the order parameter. To characterize the phase transition, we compute the
fidelity and the
  spin-Hall conductance of the open system.
  Our approach provides crucial informations for experimental implementations,
such as
  the dependence of the critical time on the system-bath coupling.
