The awake mammalian brain is functionally organized in terms of large-scale distributed networks that are constantly interacting. Loss of consciousness might disrupt this temporal organization leaving patients unresponsive. We hypothesize that characterizing brain activity in terms of transient events may provide a signature of consciousness. For this, we analyze temporal dynamics of spatiotemporally overlapping functional networks obtained from fMRI transient activity across different anesthetics and levels of anesthesia. We first show a striking homology in spatial organization of networks between monkeys and humans, indicating cross-species similarities in resting-state fMRI structure. We then track how network organization shifts under different anesthesia conditions in macaque monkeys. While the spatial aspect of the networks is preserved, their temporal dynamics are highly affected by anesthesia. Networks express for longer durations and co-activate in an anesthetic-specific configuration. Additionally, hierarchical brain organization is disrupted with a consciousness-level-signature role of the default mode network. In conclusion, large-scale brain network temporal dynamics capture differences in anesthetic-specific consciousness-level, paving the way towards a clinical translation of these cortical signature.