From what I remember when I used Authy briefly (Google Authenticator finally added the ability to mass import/export codes shortly after I ended up trying Authy), you create a login and set a master password, and then you have access to your codes on any device when you log into the app. Of course, this means that you have to trust Authy with your codes being stored externally, but this might be one of the sets of circumstances where that's preferable.