  The conflicting observations in the highly anisotropic Bi2Sr2CaCu2O8+x,
vidence for BKT behavior emerging from magnetization data and smeared 3D-xy
behavior, stemming form the temperature dependence of the magnetic in-plane
penetration depth are traced back to the rather small ratio, gsic+/gsic-=0.45,
between the c-axis correlation length probed above (+) and below (-) Tc, and
the comparatively large anisotropy. The latter leads to critical amplitudes
gsic0+,-which are substantially smaller than the distance between two CuO2
double layers. In combination with gsic+/gsic-=0.45 and in contrast to the
situation below Tc the c-axis correlation length gsic exceeds the distance
between two CuO2 double layers very close to Tc only. Below this narrow
temperature regime where 3D-xy fluctuations dominate, there is then an extended
temperature regime where the units with two CuO2 double layers are nearly
uncoupled so that 2D thermal fluctuations dominate and BKT features are
observable.
