(Abridged) We present the results of the complex study of the low surface brightness dwarf (LSBD) gas-rich galaxies J0723+3621, J0737+4724 and J0852+1350, which reside in the nearby Lynx-Cancer void. Their ratios M(HI)/L_B, according to HI data obtained with the NRT, are respectively ~3.9, ~2, ~2.6. For the two latter galaxies, we derived oxygen abundance corresponding to the value of 12+log(O/H) <~7.3, using spectra from the Russian 6m telescope and from the SDSS database. We found two additional blue LSB dwarfs, J0723+3622 and J0852+1351, which appear to be physical companions of J0723+3621 and J0852+1350 situated at the projected distances of ~12--13 kpc. The companion relative velocities, derived from the BTA spectra, are dV = +89 km/s and +30 km/s respectively. The geometry and the relative orientation of orbits and spins in these pairs indicate, respectively, prograde and polar encounters for J0723+3621 and J0852+1350. The NRT HI profiles of J0723+3621 and J0723+3622 indicate a sizable gas flow in this system. The SDSS u,g,r,i images of the five dwarfs are used to derive the photometric parameters and the exponential or Sersic disc model fits. For three of them, the (u-g),(g-r),(r-i) colours of the outer parts, being compared with the PEGASE evolutionary tracks, evidence for the dominance of the old stellar populations with ages of T ~(8-10)+-3 Gyr. For J0723+3622 and J0737+4724, the outer region colours appear rather blue, implying the ages of the oldest visible stars of T <~1-3 Gyr. The new LSB galaxies complement the list of the known most metal-poor and `unevolved dwarfs in this void, including DDO 68, SDSS J0926+3343 and others. This unique concentration of unevolved dwarf galaxies in a small cell of the nearby Universe implies a physical relationship between the slow galaxy evolution and the void-type global environment.
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