What I always do is roughly the following although you can switch this to global instead of object if you are physically compelled ;)

my $obj = MyPackage::new(); # sets $obj->{FH}=''

if ('some condition') {
    'do something about that';
    if ('another nested block') {
        open my $lh, 'etc.';
        $obj->getset('FH', $lh); # or maybe $obj->{FH}=$lh;
    }
}
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but if objects are illegal in your organisation: my $fh = '' at global scope level and update it with $lh where applicable.