With the aim of providing the complete demography of galaxies in the local Universe, including their nuclear properties, we present SPRING, a complete census of local galaxies limited to the spring quarter of the northern sky (10h < RA < 16h; 0° < Dec < 65°). The SPRING catalogue is a flux- and volume-limited sample (r < 17.7 mag, cz < 10 000 km s−1) of 30 597 galaxies, including the Virgo, Coma, and A1367 clusters. Images and spectra were individually examined to clear the sample from unwanted entries. To inspect possible secular and environmental dependencies of the various nuclear excitation properties (star-forming versus active nuclei), we performed a multi-dimensional analysis by dividing the total sample according to: (i) their position in the (NUV − i) versus Mstar diagram, (ii) the local galaxy density, (iii) the stellar mass, (iv) the halo mass of the group to which galaxies belong, and (v) the neutral hydrogen content. We present a new calibration of the optical diameter-based H I-deficiency parameter H Idef, employing a reference sample of isolated galaxies extracted from SPRING. At intermediate distances between Virgo and Coma, we identify a ring-like structure of galaxies constituted by three large filaments, each with a length of approximately 20h−1 Mpc, mostly composed of blue-cloud galaxies with stellar masses Mstar ≲ 1010 M⊙. The fraction of H I-deficient galaxies within the filament (∼30%) suggests that filaments are a transitioning environment between lower- and higher-overdensity environments in terms of H I content, as we find a clear progression from field galaxies to the filament and cluster galaxies for an increasing H Idef parameter. We classify the nuclear spectra according to the four-line Baldwin-Phillips-Terlevich (BPT) and the two-line EWHα versus [NII]/Hα (WHAN) diagnostic diagrams, and investigate the variation in the fraction of active nuclei hosts with stellar mass, as well as their colours and environments. We observe that the fraction of low-ionisation nuclear emitting regions (LINERs) is a steep function of stellar mass, for example, it is consistent with zero up to Mstar ≲ 109.5 M⊙ and becomes ∼40% for Mstar ≳ 1010.5 M⊙, whereas, for Mstar ≲ 109 − 9.5 M⊙, almost the entire spectroscopic sample is constituted of galaxies with star-forming nuclei. We investigate whether the nuclear-excitation fractions depend predominantly on the stellar mass or, conversely, on the galaxy environment. In general, we observe that the mass dependence of the fraction of Seyfert nuclei is not very sensitive to the galaxy environment, whereas the fraction of star-forming nuclei is a steeper function of stellar mass in lower-density environments and in blue-cloud galaxies. We find that the fraction of LINERs depends on galaxy colour and, for Mstar ≳ 109.5 − 10 M⊙, increases in galaxies belonging to the green valley.
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