Accurate knowledge of network topology is vital for network monitoring and management. Network tomography can probe the underlying topologies of the intervening networks solely by sending and receiving packets between end hosts: the performance correlations of the end-to-end paths between each pair of end hosts can be mapped to the lengths of their shared paths, which could be further used to identify the interior nodes and links. However, such performance correlations are usually heavily affected by the time-varying cross-traffic, making it hard to keep the estimated lengths consistent during different measurement periods, i.e., once inconsistent measurements are collected, a biased inference of the network topology then will be yielded. In this paper, we prove conditions under which it is sufficient to identify the network topology accurately against the time-varying cross-traffic. Our insight is that even though the estimated length of the shared path between two paths might be "zoomed in or out" by the cross-traffic, the network topology can still be recovered faithfully as long as we obtain the relative lengths of the shared paths between any three paths accurately.