  A space curve is determined by conformal arc-length, conformal curvature, and
conformal torsion, up to M\"obius transformations. We use the spaces of
osculating circles and spheres to give a conformally defined moving frame of a
curve in the Minkowski space, which can naturally produce the conformal
invariants and the normal form of the curve. We also give characterization of
canal surfaces in terms of curves in the set of circles.
