  The number $|K|$ of non-isotopic framed knots that correspond to a given
unframed knot $K\subset S^3$ is infinite. This follows from the existence of
the self-linking number $\slk$ of a zerohomologous framed knot. We use the
approach of Vassiliev-Goussarov invariants to construct ``affine self-linking
numbers'' that are extensions of $\slk$ to the case of nonzerohomologous framed
knots.
  As a corollary we get that $|K|=\infty$ for all knots in an oriented (not
necessarily compact) 3-manifold $M$ that is not realizable as a connected sum
$(S^1\times S^2) # M'$. This result for compact manifolds was first stated by
Hoste and Przytycki. They referred to the works of McCullough for the idea of
the proof, however to the best of our knowledge the proof of this fundamental
fact was not given in literature. Our proof is based on different ideas. For
$M=(S^1\times S^2) # M'$ we construct $K$ in $M$ such that $|K|=2\neq \infty$.
