If I understand the question, you want a separate array for each DATA SET, and each line is one array entry in the proper set.

my @array_set;
my $array;
while (<DATA>) {
   if (/^>DATA SET (\d+)) {
      $array= \$array_set[$1];
      }
   else {
      push @$array, $_;
      }
   }
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Something like that; I may have typos and such. How this works is that if a >DATA SET xxx line is seen, then $array is set to point to the proper array. Otherwise, a line is added to the current array.