Germany Italy Japan UK US
1929 to low -23.5% -3.1% -7.3% -5.8% -28.5%
year of low 1932 1933 1930 1931 1933 low to 1939 +79.1% +27.3% +71.5% +26.9% +43.2%
So, the depression was deepest and longest in the U.S. and Germany. Italy, Japan, and the UK got off fairly lightly. Germany and Japan had the strongest recoveries - a function, no doubt, of fascist Keynesianism. I can't say that this clarifies the relation, if any, between depression and world war.
Doug