AS is a collection of IP prefixes, uniquely identifies an ultimate unicast destination. Therefore you can't have the same IP belonging to multiple ASes. If you use private ASes inside your network, you just group your assigned prefixes by them and cannot propagate private AS info to the outside world.
You must use your internal routers to deal with the paths to the destinations. You can use BGP, inject (redistribute) OSPF routes to BGP or vice versa, or rely on any other IGP alone or IGPs combination. But outside world just have to know how to reach your assigned AS, nothing more.
In the case of anycast you propagate your prefix through multiple routers, belonging to your AS. The idea behind this is to route the request to closest destination. If you plan to have geographically distributed resources, then it may be a good idea to consider CDN for that.