foreach my $interval (<INTERVAL>){
       
     my @find_interval = split(/\t/, $interval);
     my $start = $find_interval[1]; 
     my $end = $find_interval[2];
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Be aware that this loop will read the entire file accessed by the  INTERVAL filehandle into memory at once as an array, each line of the file being an array element. The
    while( <INTERVAL> ) { ... }
loop reads and processes a line at a time: much more scalable, insignificant speed difference, if any.

my @find_interval = split(/\t/, $interval);

I would split directly into the named variables you will be using, and split on  '\s' (whitespace) to avoid having a newline stuck to the end of the third field element:
    my (undef, $start, $end) = split '\s', $_;