There's no built-in mechanism in Azure to facilitate blob sync'ing between regions (aside from geo-replication between paired regions). You'd need to implement this in your app. How to do this? That's subjective and would probably invite a lively discussion (plus StackOverflow isn't a place to solicit opinions).
That said... from an objective standpoint, the closest you'd find as a built-in enabler, in Azure, would be Service Bus, as it supports pub/sub. This would allow you to publish messages related to storing content, and then have subscribers representing each desired region consuming these messages from their own subscriber queue and writing to region-specific blob storage.