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Cryptocurrency systems can be subject to deanonimization attacks by exploiting the network-level communication on their peer-to-peer network. Adversaries who control a set of colluding node(s) within the peer-to-peer network can observe transactions being exchanged and infer the parties involved. Thus, various network anonymity schemes have been proposed to mitigate this problem, with some solutions providing theoretical anonymity guarantees. In this work, we model such peer-to-peer network anonymity solutions and evaluate their anonymity guarantees. To do so, we propose a novel framework that uses Bayesian inference to obtain the probability distributions linking transactions to their possible originators. We characterize transaction anonymity with those distributions, using entropy as metric of adversarial uncertainty on the originator's identity. In particular, we model Dandelion, Dandelion++ and Lightning Network. We study different configurations and demonstrate that none of them offers acceptable anonymity to their users. For instance, our analysis reveals that in the widely deployed Lightning Network, with 1% strategically chosen colluding nodes the adversary can uniquely determine the originator for about 50% of the total transactions in the network. In Dandelion, an adversary that controls 15% of the nodes has on average uncertainty among only 8 possible originators. Moreover, we observe that due to the way Dandelion and Dandelion++ are designed, increasing the network size does not correspond to an increase in the anonymity set of potential originators. Alarmingly, our longitudinal analysis of Lightning Network reveals rather an inverse trend -- with the growth of the network the overall anonymity decreases.