This paper studies the link between resting-state functional connectivity (FC), measured by the correlations of the fMRI BOLD time courses, and structural connectivity (SC), estimated through fiber tractography. Instead of a static analysis based on the correlation between SC and the FC averaged over the entire fMRI time series, we propose a dynamic analysis, based on the time evolution of the correlation between SC and a suitably windowed FC. Assessing the statistical significance of the time series against random phase permutations, our data show a pronounced peak of significance for time window widths around 20-30 TR (40-60 sec). Using the appropriate window width, we show that FC patterns oscillate between phases of high modularity, primarily shaped by anatomy, and phases of low modularity, primarily shaped by inter-network connectivity. Building upon recent results in dynamic FC, this emphasizes the potential role of SC as a transitory architecture between different highly connected resting state FC patterns. Finally, we show that networks implied in consciousness-related processes, such as the default mode network (DMN), contribute more to these brain-level fluctuations compared to other networks, such as the motor or somatosensory networks. This suggests that the fluctuations between FC and SC are capturing mind-wandering effects.