We define the Maupertuis clock which counts Kasner epochs in the Mixmaster cosmology. The characteristic time scale as measured by this clock is just the length of a given Kasner epoch. We show that in every transition from one Kasner epoch to another one unit of information is lost. Relationships of the Maupertuis time with other time parametrizations used in general relativity (cosmological time, Misner time, Chitre-Misner time, curvature time and superspace time) are investigated. In the logarithmic (mechanical) time nearby trajectories diverge linearly, and the system behaves as if it were integrable and the chaos is ``hidden'' behind this parametrization. The physical meaning of the Maupertuis time, as a chaos indicator, is discussed. We also investigate the dependence of the Lyapunov exponents on time reparametrizations.