Arbovirus can cause diseases with a broad spectrum from mild to severe and long-lasting symptoms, affecting humans worldwide and therefore considered a public health problem with global and diverse socio-economic impacts. Understanding how they spread within and across different regions is necessary to devise strategies to control and prevent new outbreaks. Complex network approaches have widespread use to get important insights on several phenomena, as the spread of these viruses within a given region. This work uses the motif-synchronization methodology to build time varying complex networks based on data of registered infections caused by Zika, chikungunya, and dengue virus from 2014 to 2020, in 417 cities of the state of Bahia, Brazil. The resulting network sets capture new information on the spread of the diseases that are related to the time delay in the synchronization of the time series among different municipalities. Thus the work adds new and important network-based insights to previous results based on dengue dataset in the period 2001–2016. The most frequent synchronization delay time between time series in different cities, which control the insertion of edges in the networks, ranges 7 to 14 days, a period that is compatible with the time of the individual-mosquito-individual transmission cycle of these diseases. As the used data covers the initial periods of the first Zika and chikungunya outbreaks, our analyses reveal an increasing monotonic dependence between distance among cities and the time delay for synchronization between the corresponding time series. The same behavior was not observed for dengue, first reported in the region back in 1986, either in the previously 2001–2016 based results or in the current work. These results show that, as the number of outbreaks accumulates, different strategies must be adopted to combat the dissemination of arbovirus infections.