The black-hole binary V404 Cyg entered the outburst phase in June 2015 after 26 years of X-ray quiescence, and with its behaviour broke the outburst evolution pattern typical of most black-hole binaries. We observed the entire outburst with the Swift satellite and performed time-resolved spectroscopy of its most active phase, obtaining over a thousand spectra with exposures from tens to hundreds of seconds. All the spectra can be fitted with an absorbed power law model, which most of the time required the presence of a partial covering. A blue-shifted iron-Kalpha line appears in 10% of the spectra together with the signature of high column densities, and about 20% of the spectra seem to show signatures of reflection. None of the spectra showed the unambiguous presence of soft disk-blackbody emission, while the observed bolometric flux exceeded the Eddington value in 3% of the spectra. Our results can be explained assuming that the inner part of the accretion flow is inflated into a slim disk that both hides the innermost (and brightest) regions of the flow, and produces a cold, clumpy, high-density outflow that introduces the high-absorption and fast spectral variability observed. We argue that the black hole in V404 Cyg might have been accreting erratically or even continuously at Eddington/Super-Eddington rates - thus sustaining a surrounding slim disk - while being partly or completely obscured by the inflated disk and its outflow. Hence, the largest flares produced by the source might not be accretion-driven events, but instead the effects of the unveiling of the extremely bright source hidden within the system.
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