The easiest way to know if a verb is transitive or intransitive, is to ask yourself "Can somebody do this verb to something?"
So "Can I bite something?" "Can I see something?" Yes I can bite things, yes I can see things. So bite and see are transitive.
"Can I sleep something?" No, I can sleep, but I can't sleep something. So sleep is INtransitive.
Can I boom something? No, an economy can boom, but nobody can 'boom' an economy, so boom is intransitive.
Of course, many verbs can be both transitive and intransitive when they have different meanings.
The bird flies. Does the bird fly someone or something? No, so this meaning is intransitive.
The pilot flies. Does the pilot fly someone or something? Yes, he flies the plane, so this meaning is transitive.
I see; thanks for suggesting your way to distinguish whether the verb we are using is transitive or intransitive.
So in my example A)"The economy of many countries around the world has been booming and flourishing" is correct;
I guess I should replace "The economy of many countries" with "The economies of many countries as well. yes?