I will talk about the work done during my PhD. This was centered on the accretion into compact object inside the framework of the induced gravitational collapse (IGC) scenario, proposed to explain the origin for the long-duration gamma-ray burst (GRBs) associated with supernovae type Ic.  In this one, a carbon-oxygen core explodes in a Type Ib/c SN in presence of a close neutron star (NS) companion. The SN  triggers an hypercritical accretion into the NS and if the accretion rate is enough high, the NS can reach its critical mass, and collapses to a black hole (BH), emitting a GRB . Otherwise, the system gives place to a x-ray flash (XRF).  With the aim to identify the separatrix of systems in which a BH is formed and characterize the observational signatures of each process, it was formulated an analytical model based in the Bondy-Hoyle accretion formalism. We also performed 3D-SPH numerical simulations of the SN expansion under the presence of the NS companion and explored a wide range of the initial parameter space.