这应该对您有用:

awk 'NR==1 { print; next } { print $0, ($1 == a && $2 == b) ? "equal" : "not_equal"; a = $1; b = $3 }' file | column -t

结果:

chr  left_pos  right_pos
1    2596      3084       not_equal
1    3084      5869       equal
1    18500     21000      not_equal
3    21000     21536      not_equal
3    22872     23179      not_equal