We have monitored the AGN 3C 390.3 between 1995 and 2000. A historical B-band light curve dating back to 1966 shows a large increase in brightness during 1970-1971, followed by a gradual decrease down to a minimum in 1982. During the 1995-2000 lapse the broad Hβ emission and the continuum flux varied by a factor of ≃3. Two large amplitude outbursts, of different duration, in continuum and Hβ light were observed i.e.: in October 1994 a brighter flare that lasted ≃1000 days and in July 1997 another one that lasted ≃700 days were detected. The response time lag of the emission lines relative to flux changes of the continuum has been found to vary with time i.e. during 1995-1997 a lag of about 100 days is evident, while during 1998-1999 a double valued lag of ≃100 days and ≃35 days is present in our data. The flux in the Hβ wings and line core vary simultaneously, a behavior indicative of predominantly circular motions in the BLR. Important changes of the Hβ emission profiles were detected: at times, we found profiles with prominent asymmetric wings, like those normaly seen in Sy1s, while at other times, we observe profiles with weak, almost symmetrical wings, similar to those of Sy1.8s. We further dismiss the hypothesis that the double peaked Hβ profiles in this object originate in a massive binary BH. Instead, we found that the radial velocity difference between the red and blue bumps is anticorrelated with the light curves of Hβ and continuum radiation. This implies that the zone that contributes most of the energy to the emitted line changes in radius within the disk. The velocity difference increases, corresponding to smaller radii, as the continuum flux decreases. When the continuum flux increases the hump velocity difference decreases. These transient phenomena are expected to result from the variable accretion rate close to the central source. The optical continuum and the Hβ flux variations might be related to changes in X-ray emission modulated by a variable accretion rate, changing the surface temperature of the disk, as a result of a variable X-ray irradiation (Ulrich, 2000, ESO Prepr., N1359, 1). Theoretical Hβ profiles were computed for an accretion disk, the observed profiles are best reproduced by an inclined disk (25°) whose region of maximum emission is located roughly at 200Rg. The mass of the black hole in 3C 390.3, estimated from the reverberation analysis is Mrev≃2.1x109M☉, 5 times larger than previous estimates (Wandel et al., 1999ApJ...526..579W).