#!/usr/local/bin/perl -w
use strict;

use Data::Dumper;

my @records;

{
    local $/ = '>'; # record separator.

    while ( <DATA> )
    {
        push( @{$records[$1]}, split(/(?:\n+|>)/) )
            if ( s/DATA SET ([0-9]+)\n+// );
    }
}

print Dumper( \@records );


__DATA__
>DATA SET 1
1aHSAJDHSDHSADHDSALHDASLDHSALDH
1bHGDKJSHDSADHSALDHLHLDHASDLSAH
1cHKJAHCADHALIDHALSDHLSADHALHDA
>DATA SET 2
2aHSAJDHSDHSADHDSALHDASLDHSALDH
2bHGDKJSHDSADHSALDHLHLDHASDLSAH
2cHKJAHCADHALIDHALSDHLSADHALHDA
>DATA SET 3
3aHSAJDHSDHSADHDSALHDASLDHSALDH
3bHGDKJSHDSADHSALDHLHLDHASDLSAH
3cHKJAHCADHALIDHALSDHLSADHALHDA