  The paper is another step towards a realisation of the goal, advanced in
articles 1706.05682 [hep-th] and 1808.04470 [hep-th], of a systematic
supersymmetry-equivariant geometrisation of physically distinguished
Green-Schwarz super-(p+2)-cocycles defining classes in the
supersymmetry-invariant refinement of the de Rham cohomology of homogeneous
spaces of (supersymmetry) Lie supergroups, associated with reductive
decompositions of their Lie superalgebras. It deals with a correlated
geometrisation of a pair of such super-(p+2)-cocycles on spaces in
correspondence under a blow-up transformation dual to the \.In\"on\"u-Wigner
contraction that relates the respective (supersymmetry) Lie superalgebras, the
latter correspondence being taken as the organising principle of the
geometrisation procedure that exploits the link between the Cartan-Eilenberg
cohomology of the supersymmetry group and the Chevalley-Eilenberg cohomology of
its Lie superalgebra, alongside a cohomological classification of central
extensions thereof. A general scheme of a correlated geometrisation compatible
with the contraction is laid out and illustrated on the nontrivial example of a
pair of consistent super-0-brane backgrounds: the super-Minkowski space
$sMink^{3,1|8}$ with the standard N=2 Green-Schwarz super-2-cocycle on it and
the super-$AdS_2 \times S^2$ space with Zhou's super-2-cocycle on it,
asymptoting to the former in the limit of an infinite common radius of the
$AdS_2$ and the $S^2$ in the body $AdS_2\times S^2$ of the supertarget. The
geometrisation yields the respective supersymmetry-equivariant super-0-gerbes,
i.e., the prequantum bundles of the associated Green-Schwarz
super-$\sigma$-models in the Nambu-Goto formulation. Upon passing to the
equivalent Hughes-Polchinski formulation of the models, the relevant extended
super-0-gerbes are verified to possess a weak $\kappa$-equivariant structure.
