We performed a systematic analysis of all INTEGRAL observations from 2003 to 2009 of 14 Supergiant Fast X-ray Transients (SFXTs), implying a net exposure time of about 30Ms. For each source we obtained lightcurves and spectra (3-100keV), discovering several new outbursts. We discuss the X-ray behaviour of SFXTs emerging from our analysis in the framework of the clumpy wind accretion mechanism we proposed (Ducci et al. 2009). We discuss the effect of X-ray photoionization on accretion in close binary systems like IGRJ16479-4514 and IGRJ17544-2619. We show that, because of X-ray photoionization, there is a high probability of formation of an accretion disk from capture of angular momentum in IGRJ16479-4514, and we suggest that the formation of transient accretion disks could be responsible of part of the flaring activity in SFXTs with narrow orbits. We also propose an alternative way to explain the origin of flares with peculiar shapes observed in our analysis applying the model of Lamb et al. (1977), which is based on the accretion via Rayleigh-Taylor instability, and was originally proposed to explain type II bursts.