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The field equations of static, spherically symmetric geometries generated by anisotropic fluids is investigated with the aim of better understanding the relation between the matter and the emergence of minimal area throats, like in wormhole and black bounce scenarios. Imposing some simplifying restrictions on the matter, which amounts to considering nonlinear electromagnetic sources, we find analytical expressions that allow one to design the type of sought geometries. We illustrate our analysis with several examples, including an asymmetric, bounded black bounce spacetime which reproduces the standard Reissner-Nordstrom geometry on the outside all the way down to the throat.

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