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We present deep spectroscopic follow-up observations of the Bremer Deep Field (BDF) where the two $z\sim$7 bright Ly$\alpha$ emitters (LAE) BDF521 and BDF3299 were previously discovered by Vanzella et al. (2011) and where a factor of $\sim$3-4 overdensity of faint LBGs has been found by Castellano et al. (2016). We confirm a new bright Ly$\alpha$ emitter, BDF2195, at the same redshift of BDF521, $z=7.008$, and at only $\sim$90 kpc physical distance from it, confirming that the BDF area is likely an overdense, reionized region. A quantitative assessment of the Ly$\alpha$ fraction shows that the number of detected bright emitters is much higher than the average found at z$\sim$7, suggesting a high Ly$\alpha$ transmission through the inter-galactic medium (IGM). However, the line visibility from fainter galaxies is at odds with this finding, since no Ly$\alpha$ emission is found in any of the observed candidates with $M_{UV}>$-20.25. This discrepancy can be understood either if some mechanism prevents Ly$\alpha$ emission from fainter galaxies within the ionized bubbles from reaching the observer, or if faint galaxies are located outside the reionized area and bright LAEs are solely responsible for the creation of their own HII regions. A thorough assessment of the nature of the BDF region and of its sources of re-ionizing radiation will be made possible by JWST spectroscopic capabilities., ERC STFC