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An investigation of the isospin equilibration process in the reactions$^{58,64}$Ni+$^{58,64}$Ni at two bombarding energies in the Fermi regime($32\,$MeV/nucleon and $52\,$MeV/nucleon) is presented. Data have been acquiredduring the first experimental campaign of the coupled INDRA-FAZIA apparatus inGANIL. Selecting from peripheral to semi-central collisions, both the neutroncontent of the quasiprojectile residue and that of the light ejectiles comingfrom the quasiprojectile evaporation have been used as probes of the dynamicalprocess of isospin diffusion between projectile and target for the asymmetricsystems. The isospin transport ratio technique has been employed. Therelaxation of the initial isospin imbalance with increasing centrality has beenclearly evidenced. The isospin equilibration appears stronger for the reactionsat $32\,$MeV/nucleon, as expected due to the longer projectile-targetinteraction time than at $52\,$MeV/nucleon. Coherent indications of isospinequilibration come from the quasiprojectile residue characteristics and fromparticles ascribed to the quasiprojectile decay.

First results from the INDRA-FAZIA apparatus on isospin diffusion in $^{58,64}$Ni+$^{58,64}$Ni systems at Fermi energies