There really isn't a way to get around this. The way a webbrowser works is that the page you were on is "trashed" while it waits for the next page to load. Each browser handles this action differently. Some hold onto the old page until they start to display information.
If you really want to remove the "white" pages, you'll learn AJAX as that can remove some of the whitepages problem. I'm not saying it's the solution, but it's a solution or work around.
You might try adding flush() somewhere in the script to push the contents that have been parsed by the PHP Parser to the browser. This may help minimize the white time. Just make sure you don't send stuff to the browser too soon, like before sessions and such.