  We refine a Le and Murakami uniqueness theorem for the Kontsevich Integral in
order to specify the relationship between the two (possibly equal) main
universal link invariants: the Kontsevich Integral and the perturbative
expression of the Chern-Simons theory. As a corollary, we prove that the
Altschuler and Freidel anomaly (that groups the Bott and Taubes anomalous
terms) is a combination of diagrams with two univalent vertices; and we
explicitly define the isomorphism of the space of Feynman diagrams which
transforms the Kontsevich Integral into the Poirier limit of the perturbative
expression of the Chern-Simons theory, as a function of the anomaly. We use
this corollary to improve the Le estimates on the denominators of the
Kontsevich Integral.
