Abstract: Computation of the Grothendieck group of 1-cycles. We now use generic transversality to compute the Grothendieck group of *semi-Fano* 1-cycles in complex threefolds.The argument is modelled on Ionel--Parker's proof of the Gopakumar--Vafa integrality conjecture.  The main sticking point is to figure out how to leverage the weaker version of generic transversality that holds in complex geometry.We may conclude, in particular, that every semi-Fano complex projective threefold is (in each homology class)enumeratively equivalent to a finite sum of local curves. This implies the MNOP conjecture for such varieties, as it is already known for local curves by work of Bryan--Pandharipande and Okounkov--Pandharipande.