Dynamic networks-networks that change over time-can be categorized into two types: offline dynamic networks, where all states of the network are known, and online dynamic networks, where only the past states of the network are known. Research on staging animated transitions in dynamic networks has focused more on offline data, where rendering strategies can take into account past and future states of the network. Rendering online dynamic networks is a more challenging problem since it requires a balance between timeliness for monitoring tasks-so that the animations do not lag too far behind the events-and clarity for comprehension tasks-to minimize simultaneous changes that may be difficult to follow. To illustrate the challenges placed by these requirements, we explore three strategies to stage animations for online dynamic networks: time-based, event-based, and a new hybrid approach that we introduce by combining the advantages of the first two. We illustrate the advantages and disadvantages of each strategy in representing low- and high-throughput data and conduct a user study involving monitoring and comprehension of dynamic networks. We also conduct a follow-up, think-aloud study combining monitoring and comprehension with experts in dynamic network visualization. Our findings show that animation staging strategies that emphasize comprehension do better for participant response times and accuracy. However, the notion of 'comprehension' is not always clear when it comes to complex changes in highly dynamic networks, requiring some iteration in staging that the hybrid approach affords. Based on our results, we make recommendations for balancing event-based and time-based parameters for our hybrid approach.