It is now well established that galaxies have different morphology, gas content and star formation rate in dense environments like galaxy clusters. The impact of environmental density extends to several virial radii, and galaxies appear to be pre-processed in filaments and groups, before falling into the cluster. Our goal is to quantify this pre-processing, in terms of gas content, and star formation rate, as a function of density in cosmic filaments. We have observed the two first CO transitions in 163 galaxies with the IRAM-30m telescope, and added 82 more measurements from the literature, for a sample of 245 galaxies in the filaments around Virgo cluster. We gathered HI-21cm measurements from the literature, and observed 69 galaxies with the Nancay telescope, to complete our sample. We compare our filament galaxies with comparable samples from the Virgo cluster and with the isolated galaxies of the AMIGA sample. We find a clear progression from field galaxies to filament and cluster ones for decreasing star formation rate, increasing fraction of galaxies in the quenching phase, increasing proportion of early-type galaxies and decreasing gas content. Galaxies in the quenching phase, defined as having star formation rate below one third of the main sequence rate, are only between 0-20% in the isolated sample, according to local galaxy density, while they are 20-60% in the filaments and 30-80% in the Virgo cluster. Processes that lead to star formation quenching are already at play in filaments. They depend mostly on the local galaxy density, while the distance to the filament spine is a secondary parameter. While the HI to stellar mass ratio decreases with local density by an order of magnitude in the filaments, and two orders of magnitude in the Virgo cluster with respect to the field, the decrease is much less for the H2 to stellar mass ratio. As the environmental density increases, the gas depletion time decreases, since the gas content decreases faster than the star formation rate. This suggests that gas depletion significantly precedes star formation quenching.