For every r∈N, we denote by θr the multigraph with two vertices and r parallel edges. Given a graph G, we say that a subgraph H of G is a model of θr in G if H contains θr as a contraction. We prove that the following edge variant of the Erd{\H o}s-P{\'o}sa property holds for every r≥2: if G is a graph and k is a positive integer, then either G contains a packing of k mutually edge-disjoint models of θr, or it contains a set S of fr(k) edges meeting all models of θr in G, for both fr(k)=O(k2r3polylog kr) and fr(k)=O(k4r2polylog kr).