We calculate the evolution of close binary systems (CBSs) formed by a neutron star (behaving as a radio pulsar) and a normal donor star, evolving either to helium white dwarf (HeWD) or ultra short orbital period systems. We consider X-ray irradiation feedback and evaporation due to radio pulsar irradiation. We show that irradiation feedback leads to cyclic mass transfer episodes, allowing CBSs to be observed in-between as binary radio pulsars under conditions in which standard, non-irradiated models predict the occurrence of a low mass X-ray binary. This behavior accounts for the existence of a family of eclipsing binary systems known as redbacks. We predict that redback companions should almost fill their Roche lobe, as observed in PSR J1723-2837. This state is also possible for systems evolving with larger orbital periods. Therefore, binary radio pulsars with companion star masses usually interpreted as larger than expected to produce HeWDs may also result in such {it quasi - Roche Lobe Overflow} states, rather than hosting a carbon-oxygen WD. We found that CBSs with initial orbital periods $mathrm{P_{i}<1}$ day evolve into redbacks. Some of them produce low mass HeWDs, and a subgroup with shorter $mathrm{P_{i}}$ become black widows (BWs). Thus, BWs descent from redbacks, although not all redbacks evolve into BWs. There is mounting observational evidence favoring that BW pulsars are very massive ($mathrm{gtrsim 2; M_{odot}}$). As they should be redback descendants, redback pulsars should also be very massive, since most of the mass is transferred before this stage.
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