Covariance comparison (box): PINOCCHIO vs. OpenGADGET3 covariance matrices, at z = 0 (left panel) and z = 1 (right panel). Shaded areas represent the numerical covariance within 1σ uncertainty, and solid lines are the semi-analytical prediction, with fitted parameters. Orange colors indicate PINOCCHIO covariance, while blue colors are for OpenGADGET3. Darker colors represent the diagonal terms, lighter colors the first off-diagonal terms. Bottom panels show the residuals of the PINOCCHIO fitted model with respect to the OpenGADGET3 one (solid line for the diagonal elements, dashed line for the off-diagonal ones).