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There were damascus barrel makers in America, but very few...relatively none, when compared to Europe and England...during the hey-day of American double production it seems as though not one American damascus maker could not compete with the Europeans makers in both numbers or cost..American makers chose the fluid steel alternative, as the Europeans eventually did.

I think part of this has to do with profitability. If you are going to start making barrels, then you will be looking to the rifle and hand gun markets as well. From at least 1890 to 1920's American policy implemented a series of tariffs on imported goods. So, the Belgians, English and German barrel makers had to be offering a unique / affordable product. In addition, makers like Heuse had American agents competing for business here.

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Didn't all heavy industry, in Liege, crash during WWI or WWII, or was Liege spared?

From the little research I have done. After WWI there was a great outcry about German atrocities in Belgium, mainly forced labor. I do not believe the factories themselves were damaged. After WWII the a lot of the heavy industry of Belgium was damaged by Allied bombing and the ground war that ensued. So there had to be a major rebuilding effort.

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If the Liege sporting gun industry wasn't interrupted during WW II, why then would the Italian gunsmiths be so desparate as to buy their tooling?

The Italians were in even worse shape after the war. A lot of damage was done during the German retreat and again the bombing campaign.

Hopefully, some one with more detailed knowledge of this period will respond.

Pete