  We describe a Dehn type surgery along a Legendrian-transverse knot K in a
bi-contact structure. We show that, when the bi-contact structure defines an
Anosov flow, there is a strong connection between the Anosovity of the new flow
and contact geometry. We give an application to the geodesic flow on the unit
tangent bundle of an hyperbolic surface. In contrast to the existing Dehn type
surgeries on contact Anosov flows, for a vast class of knots our procedure does
not require any restriction on the slope of the twist to generate new contact
Anosov flows. We finally show that there are connections between our
construction and the ones defined by Handel-Thurston, Fried-Goodman and
Foulon-Hasselblatt.
