  In this work, following [Bit15] and [Bit16a], we consider analytic singular
vector fields in $(\mathbb{C}^{3},0)$ with an isolated and doubly-resonant
singularity of saddle-node type at the origin. Such vector fields come from
irregular two-dimensional differential systems with two opposite non-zero
eigenvalues, and appear for instance when studying the irregular singularity at
infinity in Painlev{\'e} equations (P\_j), j=I...V , for generic values of the
parameters. Under suitable assumptions, we provide an analytic classification
under the action of fibered diffeomorphisms, based on the study of the Stokes
diffeomorphisms obtained by comparing consecutive sectorial normalizing maps
{\`a} la Martinet-Ramis / Stolovitch. These normalizing maps over sectorial
domains are obtained in the main theorem of [Bit16a], which is analogous to the
classical one due to Hukuhara-Kimura-Matuda for saddle-nodes in
$\mathbb{C}^{3}$. We also prove that these maps are in fact the Gevrey-1 sums
of the formal normalizing map, the existence of which has been proved in
[Bit15].
