  We study accretion rates during the gravitational wave-driven merger of a
binary supermassive black hole embedded in an accretion disc, formed by gas
driven to the centre of the galaxy. We use 3D simulations performed with
PHANTOM, a Smoothed Particle Hydrodynamics code. Contrary to previous
investigations, we show that there is evidence of a "squeezing phenomenon",
caused by the compression of the inner disc gas when the secondary black hole
spirals towards the primary. This causes an increase in the accretion rates
that always exceed the Eddington rate. We have studied the main features of the
phenomenon for a mass ratio $q = 10^{-3}$ between the black holes, including
the effects of numerical resolution, the secondary accretion radius and the
disc thickness. With our disc model with a low aspect ratio, we show that the
mass expelled from the orbit of the secondary is negligible ($< 5\%$ of the
initial disc mass), different to the findings of previous 2D simulations with
thicker discs. The increase in the accretion rates in the last stages of the
merger leads to an increase in luminosity, making it possible to detect an
electromagnetic precursor of the gravitational wave signal emitted by the
coalescence.
