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Then, we used such a covariance to define the likelihood function that is better equipped to extract cosmological information from cluster number counts at the level of precision that will be reached by the future <jats:italic>Euclid<\/jats:italic> photometric catalogs of galaxy clusters. We also studied the impact of the cosmology dependence of the covariance matrix on the parameter constraints.<\/jats:p>\n<jats:p><jats:italic>Results.<\/jats:italic> The analytical covariance matrix reproduces the variance measured from simulations within the 10 percent; such a difference has no sizeable effect on the error of cosmological parameter constraints at this level of statistics. 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