Apple provides this possibility via class UIDocumentInteractionController. It’s really simple to do. I’ll just keep here.
Example:
var controller = UIDocumentInteractionController()
let epubURL = NSBundle.mainBundle().URLForResource("test", withExtension: "epub")
controller.URL = epubURL
if !controller.presentOpenInMenuFromRect(button.bounds, inView: view, animated: true) {
print("You don't have an app installed that can handle ePub files.")
}
A class UIDocumentInteractionController has other features, you can read more details in Apple documentation.