We show there exists a closed graph manifold N and infinitely many non-separable, horizontal surfaces { S n ↬ N } n ∈ ℕ such that there does not exist a quasi-isometry π 1 (N) → π 1 (N) taking π 1 (S n) to π 1 (S m) within a finite Hausdorff distance when n ≠ m.