  The diffractive electro- or photo-production of two mesons separated by a
large rapidity gap gives access to generalized parton distributions (GPDs) in a
very specific way. First, these reactions allow to easily access the chiral-odd
transversity quark GPDs by selecting one of the produced vector meson to be
transversely polarized. Second, they are only sensitive to the so-called ERBL
region where GPDs are not much constrained by forward quark distributions.
Third, the skewness parameter $\xi$ is not related to the Bjorken $x_\text{Bj}$
variable, but to the size of the rapidity gap. We analyze different channels
($\rho_L^0\,\rho_{L/T}, \rho^0_L\,\omega_{L/T}$ and $\rho^0_L\,\pi$ production)
on nucleon and deuteron targets. The analysis is performed in the kinematical
domain where a large momentum transfer from the photon to the diffractively
produced vector meson introduces a hard scale (the virtuality of the exchanged
hard Pomeron). This enables the description of the hadronic part of the process
in the framework of collinear factorization of GPDs. We show that the
unpolarized cross sections depend very much on the parameterizations of both
chiral-even and chiral-odd quark distributions of the nucleon, as well as on
the shape of the meson distribution amplitudes. The rates are shown to be in
the range of the capacities of a future electron-ion collider.
