  We have studied the field-induced dimensional crossover in the fluctuation
magnetization of three single crystals of $YBa_2Cu_3O_{7-x}$, with
superconducting transition temperatures, $T_c$= 62.5, 52, and 41 K. The
dimensional crossover is observed by studying the diamagnetic vortex
fluctuations of the lowest-Landau-level type which occur in isochamps
magnetization curves, $MvsT$, for temperatures close to the transition
temperature $T_{c}(H)$. The study was accomplished by obtaining isochamps
magnetization curves as a function of temperature for fields in the range of
0.4 T to 5 T. Magnetization curves for each sample when plotted together show
two distinct well resolved crossing points, one formed by low field curves and
located at a higher temperature than the other formed by high field curves. A
lowest-Landau-level scaling analysis is applied to the curves forming the
crossing points and it is verified that lower field curves obey the
three-dimensional form of this scaling while the higher field curves obey the
two-dimensional form. The results allow to observe the evolution of the
dimensional crossover field $H_{cross}$, 3D-2D, with the content of oxygen in
$YBa_2Cu_3O_{7-x}$. It is observed that the evolution of the field $H_{cross}$
with the content of oxygen in each sample qualitatively agrees with theoretical
predictions and allow us to estimate the ratio of the anisotropy among the
studied samples. \\pacs{74.40.+k}
