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This work presents the first results of the Deep IFS View of Nuclei of Galaxies (DIVING$^\mathrm{3D}$) survey. We analysed the nuclear emission-line spectra of a sub-sample we call mini-DIVING$^\mathrm{3D}$, which includes all Southern galaxies with B < 11.2 and |b| > 15 degrees. We verified that $23\% \pm 4\%$ of the galaxies show nuclear emission-line properties characteristic of Low Ionization Nuclear Emission-Line Regions (LINERs). Diagnostic diagram analysis reveals an apparent dichotomy, not detected in previous studies, between objects classified as H II regions and as LINERs or Seyferts, with very few galaxies classified as transition objects. A possible explanation for this result is that at least part of the transition objects are composite systems, with a central LINER contaminated by the emission from circumnuclear H II regions. The higher spatial resolution of the DIVING$^\mathrm{3D}$ survey, in comparison with previous studies, allowed us to isolate the nuclear emission from circumnuclear contaminations, reducing the number of transition objects. We also propose an alternative scenario, in which the emission-line spectra of some transition objects are the result of shock heating by central outflows, together with photoionization by young stars. Clear evidence of active galactic nuclei (AGNs), in the optical and X-ray spectral bands, were detected in 69$\%$ of the LINERs in the mini-DIVING$^\mathrm{3D}$ sample. Considering the entire mini-DIVING$^\mathrm{3D}$ sample, evidence of AGNs were detected in 65$\%$ of the objects.