  We show that the Euclidean and Lorentzian EPRL vertex amplitudes of covariant
Loop Quantum Gravity are related through a ``Wick rotation'' of the real
Immirzi parameter to purely imaginary values. Our result follows from the
simultaneous analytic continuation of the algebras, group elements and unitary
irreducible representations of the gauge groups $Spin(4)$ and
$SL(2,\mathbb{C})$, applied to the decomposition of the two models in terms of
$SU(2)$ invariants and booster functions.
