Last week’s blog dealt with how a mosaic dataset handles different projections. In response to that blog, there were several of users that then wondered how a mosaic dataset handles data with different geographic transformations.
In order for a mosaic dataset to properly handle data with various transformations, you will need to specify all the geographic transformations that the mosaic dataset needs to accommodate.
How do you specify a geographic transformation?
1) In the ArcMap Catalog Window, right-click on the mosaic dataset, and click on Properties.
2) Click on the Defaults tab.
3) Scroll to the bottom of the window.
4) Click on the ellipsis button (…), which is beside Geographic Coordinate System Transformation. 
5) Check if the geographic transformation that you need is populated in the list.
6) If it is not there, choose a geographic transformation that is relevant to the data in your mosaic dataset and click the Add Item (plus sign).
7) If all the geographic transformations have been set, then click OK to accept your specified transformations.
Written by: Simon W.