The aim of this thesis is to explore the Universe at low surface brightness on a large sample of galaxies in the nearest cosmic filaments (z<0.1) by exploiting the unique imaging and spectroscopy capabilities of Euclid, a mission that will be launched in 2023 by the European Space Agency and in which France is heavily involved. Cosmological simulations and theoretical models predict a morphological segregation of galaxies at the edge and within the large filaments that form the cosmic web, as well as notable correlations between their orientation and that of the large cosmic filaments. This segregation results from tidal effects via i) the infall of galaxies towards the gravitational potential wells caused by the dark matter of the filaments and ii) the flow of galaxies within these same filaments. To date, this signature has not been explored in depth in the nearby Universe because of a lack of an adequate large imaging+spectroscopic survey. However, understanding these intrinsic alignments of galaxies has a twofold interest, not only to understand the formation and evolution of galaxies as such (nature vs nurture) but also because these alignments contaminate the cosmic shear signal which is measured from coherent deformations of the shapes of galaxies. Thus, the Euclid space telescope will constrain the evolution models of the Universe while providing evidence on the intrinsic alignments of galaxies which affect at higher redshift the measurements of gravitational shear at the heart of the Euclid’s core science on the question of dark energy. Recent advances in the exploration of the outer regions of galaxies indicate that the morphology inferred from the central, bright, section generally does not reflect the one derived from the outermost regions related to the halo. These outer regions are a tracer of the evolution over the last billion years during which galaxies have evolved within, or near, a large structure, the interactions between galaxies in the filament representing a nuisance factor. The nearby Universe is the ideal laboratory because the cosmological extinction still has little effect on the measurement of the faint brightness of the external regions of the galaxies. Euclid will provide a unique sample of galaxies whose membership in filaments will be guaranteed by spectroscopy while its imaging capabilities at low surface brightness from the optical to the near-infrared (a whole new observation window ideal for capturing the old stellar population from the outer regions) will reveal the morphology at the true edges of the galaxies. This project is a rare case in the Euclid legacy science making a critical use of all three instrumental modes, exploiting the VIS, Y, H, J imaging and the spectroscopy. Before focusing this study on the Euclid data which will arrive in 2024, the first part of the thesis will consist in a pilot study based on data from the CFIS-UNIONS northern sky survey carried out with the MegaCam camera on the Canada-France-Hawaii Telescope. This ground-based survey spawned from the need of securing photometric data to derive photometric redshifts for Euclid but it also carries a diverse galactic and extragalactic science that stands on its own merit. The pilot study will exploit this deep optical dataset optimized for low surface brightness studies in particular, over an area that covers the nearest dense filament, the Pisces-Perseus supercluster at z=0.02 covering 80 degrees (!) in the sky. The full imaging dataset has now been acquired over this region of interest and is ready for analysis in the context of a thesis effort. Spectroscopic redshifts are available for nearly two thousand galaxies from the Sloan surveys and the HI Arecibo Legacy Fast ALFA Survey. The CFIS-UNIONS survey, just as Euclid will, also probes the large voids around the filament, thus completing the comparison of morphology segregation of galaxies directly linked to the filament.