Just sed and nl and sort :
nl <filename> -s ":"|sort -t ":" -k 3 -k 2 | sed -n ":x s/\n[0-9 ]*$//;/end[^\n]*$/{N;bx};s/\(.*\)[ 0-9]*:end .*id:\( [0-9]*\).*\n.*start.*id:\2[^0-9]*$/\1/;tx;s/\n$//;/start/{P;D};/^[ 0-9]*:end[^\n]*/{s/\n[0-9:]*$/$/;N;bx};/start/P;/end/P;" | sort -n| sed "s/[ 0-9]*://"
nl tt -s ":"|sort -t ":" -k 3 -k 2 | sed -n ":x s/\n[0-9 ]*$//;/end[^\n]*$/{N;bx};s/\(.*\)[ 0-9]*:end .*id:\( [0-9]*\).*\n.*start.*id:\2[^0-9]*$/\1/;tx;s/\n$//;/start/{P;D};/^[ 0-9]*:end[^\n]*/{s/\n[0-9:]*$/$/;N;bx};/start/P;/end/P;" | sort -n| sed "s/[ 0-9]*://"
start ======== id: 5713
start ======== id: 5713
start ======== id: 5713
start ======== id: 5713
start ======== id: 5911
start ======== id: 6111
end ======== id: 31117
If the order is not important (and if every end has the start line):
sort <filename> -t ":" -k 2|sed -e '/end/{N;d;}
start ======== id: 31117
start ======== id: 5911
start ======== id: 6111
This is better (need to repair, but working):
sort <filename> -t ":" -k 2 | sed -n ":x ;/end[^\n]*$/{N;bx};s/\(.*\)end .*id:\( [0-9]*\).*start.*id:\2[^0-9]*$/\1/;tx;s/\n$//;/start/{P;D};/^end[^\n]*/{s/\n$/$/;N;bx};/start/P;/end/P"
cat tt
start ======== id: 5713
start ======== id: 5713
start ======== id: 5713
start ======== id: 5713
start ======== id: 5713
start ======== id: 5713
start ======== id: 5713
dggdgtfZZ
start ======== id: 5713
start ======== id: 5713
start ======== id: 5911
start ======== id: 5911
end ========= id: 5911
start ======== id: 6111
end ========= id: 5713
end ========= id: 5713
end ========= id: 5713
end ========= id: 5713
end ========= id: 5713
start ======== id: 31117
end ======== id: 31117
end ======== id: 31117
sort -t ":" -k 2 tt| sed -n ":x ;/end[^\n]*$/{N;bx};s/\(.*\)end .*id:\( [0-9]*\).*start.*id:\2[^0-9]*$/\1/;tx;s/\n$//;/start/{P;D};/^end[^\n]*/{s/\n$/$/;N;bx};/start/P;/end/P"
end ======== id: 31117
start ======== id: 5713
start ======== id: 5713
start ======== id: 5713
start ======== id: 5713
start ======== id: 5911
start ======== id: 6111