  The primary formation channel for the stellar-mass Binary Black Holes which
have been detected merging by the LIGO-Virgo-KAGRA (LVK) collaboration is yet
to be discerned. One of the main obstacles is that such Gravitational Wave (GW)
events are not in general expected to produce an Electromagnetic (EM)
counterpart. This might not be the case if the mergers happen in gaseous
environments, such as the accretion discs of Active Galactic Nuclei (AGN).
Recently, 20 AGN flares detected by the Zwicky Transient Facility have been
investigated as potential counterparts of GW events by Graham et al. (2023). We
present a new spatial correlation analysis involving such events that uses the
up-to-date posterior samples of 78 mergers detected during the third observing
run of the LVK collaboration. We apply a likelihood method which takes into
account the exact position of the EM signal within the 3D sky map of the GW
events. We find that current data favour the hypothesis of no causal connection
between the detected mergers and the AGN flares. We place an upper limit of
0.155 at a 90 per cent credibility level on the fraction of coalescences that
are physically related to a flare. Moreover, we show that the mass distribution
of the merging binaries that appear in coincidence with AGN flares,
characterised by values typically larger than the ones of the full population
of GW events, is also consistent with the no-connection hypothesis. This is
because of a positive correlation between the binary mass and the
reconstruction volume.
