  This paper deals with the properties of the stochastic generators of the
effective (driven) processes associated with atypical values of
transition-dependent time-integrated currents with Gallavotti-Cohen symmetry in
Markov jump processes. Exploiting the concept of biased ensemble of
trajectories by introducing a biasing field $s$, we show that the stochastic
generators of the effective processes associated with the biasing fields $s$
and $E-s$ are enantiodromic with respect to each other where $E$ is the
conjugated field to the current. We illustrate our findings by considering an
exactly solvable creation-annihilation process of classical particles with
nearest-neighbor interactions defined on a one-dimensional lattice.
