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The paper is another step towards a realisation of the goal, advanced inarticles 1706.05682 [hep-th] and 1808.04470 [hep-th], of a systematicsupersymmetry-equivariant geometrisation of physically distinguishedGreen-Schwarz super-(p+2)-cocycles defining classes in thesupersymmetry-invariant refinement of the de Rham cohomology of homogeneousspaces of (supersymmetry) Lie supergroups, associated with reductivedecompositions of their Lie superalgebras. It deals with a correlatedgeometrisation of a pair of such super-(p+2)-cocycles on spaces incorrespondence under a blow-up transformation dual to the \.In\"on\"u-Wignercontraction that relates the respective (supersymmetry) Lie superalgebras, thelatter correspondence being taken as the organising principle of thegeometrisation procedure that exploits the link between the Cartan-Eilenbergcohomology of the supersymmetry group and the Chevalley-Eilenberg cohomology ofits Lie superalgebra, alongside a cohomological classification of centralextensions thereof. A general scheme of a correlated geometrisation compatiblewith the contraction is laid out and illustrated on the nontrivial example of apair 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 andthe 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. Thegeometrisation yields the respective supersymmetry-equivariant super-0-gerbes,i.e., the prequantum bundles of the associated Green-Schwarzsuper-$\sigma$-models in the Nambu-Goto formulation. Upon passing to theequivalent Hughes-Polchinski formulation of the models, the relevant extendedsuper-0-gerbes are verified to possess a weak $\kappa$-equivariant structure.

Equivariant prequantisation of the super-0-brane in ${\rm AdS}_2\times\mathbb{S}^2$ - a toy model for supergerbe theory on curved spaces