How to map a domain to a subdomain of my current blog?

Hi, all,
I have installed 3.2.1 wp with multiple site in sub-domain enabled. So I have a site like: mysite.com, and blog.mysite.com. Now I want to buy another new top domain, let’s call it mytopdog.com and I want mytopdog.com points to blog.mysite.com.
So, whenever user goes to mytopdog.com, it is actually also on blog.mysite.com, but user won’t see mysite.com at all. That way I can manage all blogs in one place at mysite.com. How do I do that?
(I am with hostgator)

Thanks