To avoid URL changes or downtime SharePoint 2013 during upgrade, you might need to redirect old site collection URLs to new URLs. There are several techniques you could choice depends on different situation. Here is the summary of these options and the situation you might use.
1. The best option is do not redirect. You could use the same VIP and point to the new SharePoint 2013 servers that will only require infrastructure changes like load balance configuration change. Example is the http://sharepoint used in SharePoint 2010 will point to new 2013 servers.
This option can be used if you migrate SharePoint farm all site collections at one time and you have VIP set up originally.
2. The second option is DNS redirect. You could update DNS entries to point the oldserver to new server. This will only need DNS entry change and no other configuration needed.
This option can be used if you migrate SharePoint farm all site collections at one time and you do not have VIP in place.
3. The third option is to use IIS redirect. You could set IIS redirect rules to redirect specific URL patterns to new servers. You could refer the instruction to configure URL redirect rules. This option you have to have old IIS that are used for previous SharePoint version running in order to support redirect.The IIS redirect rule syntax is little tricky to set up exactly want you want.
This option can be used if you migrated partial site collections and could like to redirect only those site collections.
4. The forth option is to utilize AAM redirect. You could use powershell set up for specific webapp to redirect any site not found on existing webapp to new webapp. The new webapp could be on same server farm or different new SharePoint farm. You could need to setup once and it will work for all site collections inside the same webapp.
This option can be used if you migrated partial site collections and could like to redirect only those site collections.This redirect is different from option 3 since SharePoint will try to find the site collection under correct webapp, it will redirect to different webapp if the site collection not exist. This is very useful and I'll explain in details in next blog.
5. The fifth option is to modify the default page Default.aspx to redirect to different site collection or site as described by Harmeet Walia from Microsoft.
This option can be used if you migrated partial site collections and could like to redirect only those site collections. It will work for any sub-sites also that is advantage.
The option you choice will depend on your migration situation. You might use option 4 first during migration and use option 1 after migration completed.