The company migrated its Analytics data from Citus Cloud on Amazon's AWS to Citus on Microsoft Azure after learning about Microsoft's acquisition of Citus Data. The migration process involved creating a comprehensive playbook, conducting comparative analysis and testing each part of the pipeline separately. Some challenges encountered during the migration included differences in file systems between AWS and Azure, regression in writing to HyperScale (Citus), and an unexpected "duplicate key" error due to different versions of libc on Azure. The migration process was successful with no downtime, highlighting the importance of thorough planning, testing, and teamwork.