  In this article we investigate an interpolating gauge fixing procedure in
$(4l+3)$-dimensional abelian Chern-Simons theory. We show that this
interpolating gauge is related to the covariant gauge in a constant anisotropic
metric. We compute the corresponding propagators involved in various
expressions of the linking number in various gauges. We comment on the
geometric interpretations of these expressions, clarifying how to pass from one
interpretation to another.
