One way:

#!perl
use strict;
use warnings;

while (<DATA>) {
  if (my ($bbegin) = /^(=+KEYWORD \d+)/) {
    my $block_o_text;
    while (1) {
      $_ = <DATA>;
      /^${bbegin}_END/ ? last : ($block_o_text .= $_);
    }
    print "Do something with $block_o_text\n";
  }
}
__DATA__
========KEYWORD 1===========
Text
text
text
========KEYWORD 1_END=======


========KEYWORD 2===========
Text
text
text
========KEYWORD 2_END=======


========KEYWORD 3===========
Text
text
text
========KEYWORD 3_END=======
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