only when the labels in the Group by for that report is not displaying information
Don't know what that means, because labels don't show data ("information"). They only show captions. Perhaps you mean you don't want page header labels to show if a group on the page has no data. I have no idea on how to do that but it might be doable if there is only one group on a page. At this point, I don't see what ties any group to the header labels.
which has the same labels
This is not possible, but it is possible that group labels and page header labels have the same captions.
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.