Or to make it easier: you just want to disable the caching in order to see your changes in realtime.
Any solution that would allow you to disable caching based on IP, logged user or cookie will be acceptable.
How can you develop on a live WordPress installation that is using W3 Total Cache?
It has this natively: Performance > Page Cache > General > Don’t cache pages for logged in users
You can always check if you are seeing cached page by looking at page source, W3 outputs status (commented out) at end of page.
Also, I would recommend against developing on a live site. Do all of your development on a private (i.e. local) installation of WordPress, then update your live installation and purge the cache. Developing on a live site runs the risk of breaking something for users while they’re using the site!