API Connect

Now customer has one question for below OVA setup in production. Can customer stop the Analytics data synchronization between Data Center 1 and Data Center 2 for certain period (e.g. 2 months)? After 2 months, customer wants to delete the Analytics data from Data Center 2 and then resuming the Analytics data synchronization between data center 1 and data center 2. When resuming the process, all Analytics data in data center 1 need to be synced to data center 2. 

I think you have misunderstood that architecture.

that diagram shows apim and portal synchronisation but analytics and gateways are two independent services. There will be no data synchronisation of analytics.

If you did somehow achieve that then there definitely is not a way to selectively remove data from analytics. There is definitely no way to sync/export all of the existing data in analytics either.

This is not a supported scenario.