The role of the cosmic web in shaping galaxy properties is investigated in the GAMA spectroscopic survey in the redshift range 0.03 z 0.25. The stellar mass, u − r dust corrected colour and specific star formation rate (sSFR) of galaxies are analysed as a function of their distances to the 3D cosmic web features, such as nodes, filaments and walls, as reconstructed by DisPerSE. Significant mass and type/colour gradients are found for the whole population, with more massive and/or passive galaxies being located closer to the filament and wall than their less massive and/or star-forming counterparts. Mass segregation persists among the starforming population alone. The red fraction of galaxies increases when closing in on nodes, and on filaments regardless of the distance to nodes. Similarly, the star-forming population reddens (or lowers its sSFR) at fixed mass when closing in on filament, implying that some quenching takes place. Comparable trends are also found in the state-of-the-art hydrodynamical simulation HORIZON-AGN. These results suggest that on top of stellar mass and large-scale density, the traceless component of the tides from the anisotropic large-scale environment also shapes galactic properties. An extension of excursion theory accounting for filamentary tides provides a qualitative explanation in terms of anisotropic assembly bias: at a given mass, the accretion rate varies with the orientation and distance to filaments. It also explains the absence of type/colour gradients in the data on smaller, non-linear scales.

The mass, accretion rate and formation time of dark matter haloes near proto-filaments (identified as saddle points of the potential) are analytically predicted using a conditional version of the excursion set approach in its so-called "upcrossing" approximation. The model predicts that at fixed mass, mass accretion rate and formation time vary with orientation and distance from the saddle, demonstrating that assembly bias is indeed influenced by the tides imposed by the cosmic web. Starved, early forming haloes of smaller mass lie preferentially along the main axis of filaments, while more massive and younger haloes are found closer to the nodes. Distinct gradients for distinct tracers such as typical mass and accretion rate occur because the saddle condition is anisotropic, and because the statistics of these observables depend on both the conditional means and their covariances. The theory is extended to other critical points of the potential field. The response of the mass function to variations of the matter density field (the so-called large scale bias) is computed, and its trend with accretion rate is shown to invert along the filament.The signature of this model should correspond at low redshift to an excess of reddened galactic hosts at fixed mass along preferred directions, as recently reported in spectroscopic and photometric surveys and in hydrodynamical simulations. The anisotropy of the cosmic web emerges therefore as a significant ingredient to describe jointly the dynamics and physics of galaxies, e.g. in the context of intrinsic alignments or morphological diversity.