Swift has allowed the possibility to give Supergiant Fast X-ray Transients (SFXTs), the new class of High Mass X-ray Binaries discovered by INTEGRAL, non serendipitous attention throughout all phases of their life. We present our results based on the first year of intense Swift monitoring of four SFXTs, IGR J16479-4514, XTE J1739-302, IGR J17544-2619 and AX J1841.0-0536. We obtain the first assessment of how long each source spends in each state using a systematic monitoring with a sensitive instrument. The duty-cycle of inactivity is 17, 28, 39, 55% (5% uncertainty), for IGR J16479-4514, AX J1841.0-0536, XTE J1739-302, and IGR J17544-2619, respectively, so that true quiescence is a rare state. This demonstrates that these transients accrete matter throughout their life at different rates. AX J1841.0-0536 is the only source which has not undergone a bright outburst during our campaign. Although individual sources behave somewhat differently, common X-ray characteristics of this class are emerging such as outburst lengths well in excess of hours, with a multiple peaked structure. A high dynamic range (including bright outbursts) of 4 orders of magnitude has been observed. We performed out-of-outburst intensity-based spectroscopy. Spectral fits with an absorbed blackbody always result in blackbody radii of a few hundred meters, consistent with being emitted from a small portion of the neutron star surface, very likely the neutron star polar caps. We also present the UVOT data of these sources. (Abridged)
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