We present an in-depth analysis of the spectral and temporal behavior of a long almost uninterrupted INTEGRAL observation of Vela X-1 in Nov/Dec 2003. In addition to an already high activity level, Vela X-1 exhibited several very intense flares with a maximum intensity of more than 5 Crab in the 20 40 keV band. Furthermore Vela X-1 exhibited several off states where the source became undetectable with ISGRI. We interpret flares and off states as being due to the strongly structured wind of the optical companion: when Vela X-1 encounters a cavity in the wind with strongly reduced density, the flux will drop, thus potentially triggering the onset of the propeller effect which inhibits further accretion, thus giving rise to the off states. The required drop in density to trigger the propeller effect in Vela X-1 is of the same order as predicted by theoretical papers for the densities in the OB star winds. The same structured wind can give rise to the giant flares when Vela X-1 encounters a dense blob in the wind. Further temporal analysis revealed that a short lived QPO with a period of 6800 sec is present. The part of the light curve during which the QPO is present is very close to the off states and just following a high intensity state, thus showing that all these phenomena are related
