Pre_Transition refers to Barling pipes made while the family owned the business. In October of 1960, the Barling family sold their business to Finlay, who had been one of their largest clients. That period was referred to as the "Transition" era. Then Imperial Tobacco took over Barling and that is the "Post_Transition" era.
That was the traditional definition until last year, when new scholarship by Jon Guss provided a somewhat different story, one that makes the traditional definitions inaccurate.
It's simpler and more accurate to refer to Barling pipes as either "Family Era" and either "Post Family" or "Corporate" era.
Family Era pipes were made from 1812 to 1962, when the Barling family left the business, a full 20 months after selling it to Finlay. Finlay, which was 40% owned by Imperial Tobacco, was "absorbed" by Imperial tobacco in February of 1963. So there no real "Transition" Era.
If you want to know more about Barling pipes I suggest that you read the Pipedia Barling page, which I largely wrote, and Jon Guss's fabulous article "How Many Angels" which is to be found in the "vintages" section of Neill Archer Roan's excellent site, "A Passion For Pipes".