The best option that uses transitions most effectively is:
"On one hand, a society needs to identify the poor to understand its health. On the other hand, a government needs to define what it means to be poor for help. Fortunately, there is more than one kind of poverty. To illustrate, consider absolute poverty or the minimum income needed to buy the bare necessities of food, clothing, and shelter. It is a fixed standard based on minimum needs for survival. It is possible for no one to be in absolute poverty. In comparison, relative poverty is income compared to what others in the community earn. It determines poverty on a curve. Someone will always be in relative poverty. Someone will always have less income."
This paragraph effectively employs transitional phrases that clarify the relationships between ideas, such as "On one hand," "On the other hand," "Fortunately," "To illustrate," and "In comparison." These help guide the reader through the argument and enhance coherence in the writing.