sed to find a block of text

How do I address all the lines between RE1 and RE2, excluding
the lines themselves?

Normally, to address the lines between two regular expressions, RE1
and RE2, one would do this: '/RE1/,/RE2/{commands;}'. Excluding
those lines takes an extra step. To put 2 arrows before each line
between RE1 and RE2, except for those lines:
sed '1,/RE1/!{ /RE2/,/RE1/!s/^/>>/; }' input.fil
The preceding script, though short, may be difficult to follow. It
also requires that /RE1/ cannot occur on the first line of the
input file. The following script, though it's not a one-liner, is
easier to read and it permits /RE1/ to appear on the first line:

/RE1/,/RE2/{
/RE1/b
/RE2/b
s/^/>>/
}

A solution to the problem :

sed -n -e '/A/,/B/{
/A/b
/B/b
p
}' File > Target_file

The same thing with awk

awk '/A/,/B/{ if (/A/ || /B/) next; print }' F > G