  We study new classes three dimensional black hole solutions of Einstein
equations written in two holonomic and one anholonomic variables with respect
to anholonomic frames Thermodynamic properties of such (2+1)-black holes with
generic local anisotropy (having elliptitic horizons) are studied by applying
geometric methods. The corresponding thermodynamic systems are three
dimensional with entropy S being a hypersurface function on mass M, anisotropy
angle $\theta$ and eccentricity of elliptic deformations $\epsilon >.$
Two-dimensional curved thermodynamic geometries for locally anistropic deformed
black holes are constructed after integration on anisotropic parameter
$\theta$. Two approaches, the first one based on two-dimensional hypersurface
parametric geometry and the second one developed in a
Ruppeiner-Mrugala-Janyszek fashion, are analyzed. The thermodynamic curvatures
are computed and the critical points of curvature vanishing are defined.
