Transversality in generalized manifolds

Suppose that X is a generalized n-manifold, n≥5, satisfying the disjoint disks property, and M and Q are topological m- and q-manifolds, respectively, 1-LCC embedded in X, with n−m≥3 and n−q≥3. We define what it means for M to be stably transverse to Q in X. In the metastable range, 3m≤2(n−1) and 3(m+q)<4(n−1), we show that there is an arbitrarily small homotopy of M to a 1-LCC embedding that is stably transverse to Q.