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Lisca classified the Stein fillings of $(L(p,q), \\xi_{st})$ up to diffeomorphisms and conjectured that they correspond bijectively through an {\\it explicit} map to the Milnor fibers associated with the irreducible components (all of them being smoothing components) of the reduced miniversal space of deformations of $\\mathcal{X}_{p,q}$. 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