  Short gamma-ray bursts originate when relativistic jets emerge from the
remnants of binary neutron star mergers. Both the jet and the remnant are
believed to be strongly magnetized, and the presence of magnetic fields is
known to influence the jet propagation across the surrounding post-merger
environment. In the magnetic interplay between the jet and the environment
itself, effects due to a finite plasma conductivity may be important,
especially in the first phases of the jet propagation. We aim to investigate
such effects, from jet launching to its final breakout from the post-merger
environment. 2D axisymmetric and full 3D resistive relativistic MHD
simulations, are performed with the PLUTO numerical code. Different models for
physical resistivity, which must be small but still above the numerical one
(producing unwanted smearing of structures in any ideal MHD code) are
considered and compared. All simulations are performed by using an axisymmetric
analytical model for the jet propagation environment; we leave the case of jet
propagation in a realistic environment (i.e. imported from actual binary
neutron star merger simulation) to a later study. Significant differences in
the jet structure and induced turbulence are clearly seen in 2D axisymmetric
simulations. Regions with a resistive electric field parallel to the magnetic
field form and non-thermal particle acceleration may be enhanced there. The
level of dissipated Ohmic power is also dependent on the various recipes for
resistivity. Most of the differences arise before breakout from the magnetized
environment, whereas once the jet enters the external atmosphere these
differences are preserved during further propagation despite the lower grid
refinement. Finally, we show and discuss the 3D evolution of the jet within the
same environment, in order to highlight the emergence of non-axisymmetric
features.
