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Models of inhomogeneous universes constructed with exact solutions ofEinstein's General Relativity have been proposed in the literature with the aimof reproducing the cosmological data without any need for a dark energycomponent. Besides large scale inhomogeneity models spherically symmetricaround the observer, Swiss-cheese models have also been studied. Among them,Swiss-cheeses where the inhomogeneous patches are modeled by differentparticular Szekeres solutions have been used for reproducing the apparentdimming of the type Ia supernovae (SNIa). However, the problem of fitting suchmodels to the SNIa data is completely degenerate and we need other constraintsto fully characterize them. One of the tests which is known to be able todiscriminate between different cosmological models is the redshift-drift. Thisdrift has already been calculated by different authors forLema\^itre-Tolman-Bondi (LTB) models. We compute it here for one particularaxially symmetric quasi-spherical Szekeres (QSS) Swiss-cheese which haspreviously been shown to reproduce to a good accuracy the SNIa data, and wecompare the results to the drift in the $\Lambda$CDM model and in some LTBmodels that can be found in the literature. We show that it is a gooddiscriminator between them. Then, we discuss our model's remaining degrees offreedom and propose a recipe to fully constrain them.

Redshift drift in axially symmetric quasi-spherical Szekeres models