Dengue-fever, Zika, and chikungunya are arboviral infection diseases transmitted mainly by two vectors: Aedes aegypti and Aedes albopictus. We have available the weekly number of cases of each of the diseases across the 163 neighborhoods of Rio de Janeiro, between August 2015 and June 2016. During this period the city experienced an epidemic of the three diseases which started at different weeks for each of the diseases. We aim at understanding the evolution, and possible correlations, of the diseases across time and space. We have information available on the weekly variation of environmental covariates, and socio-economic covariates at the neighborhood level. We propose a Poisson multivariate spatio-temporal model that allows the associations between the covariates and the logarithm of the relative risk to vary with the disease. The main challenge is to understand the structure left in the log-relative risk after accounting for the covariates. We explore different latent spatio-temporal effects that account for the irregular size of the neighborhoods, and different correlation structures among the diseases, across space and time.