  The perturbative expansion of Chern-Simons gauge theory leads to invariants
of knots and links, the finite type invariants or Vassiliev invariants. It has
been proven that at any order in perturbation theory the resulting expression
is an invariant of that order. Bott-Taubes integrals on configuration spaces
are introduced in the present context to write Feynman diagrams at a given
order in perturbation theory in a geometrical and topological setting. One of
the consequences of the configuration space formalism is that the resulting
amplitudes are given in cohomological terms. This cohomological structure can
be used to translate Bott-Taubes integrals into Chern-Simons perturbative
amplitudes and vice versa. In this article this program is performed up to
third order in the coupling constant. This expands some work previously worked
out by Thurston. Finally we take advantage of these results to incorporate in
the formalism a smooth and divergenceless vector field on the $3$-manifold. The
Bott-Taubes integrals obtained are used for constructing higher-order
asymptotic Vassiliev invariants extending the work of Komendarczyk and Voli\'c.
