"drizzle $\rightarrow$ rain $\rightarrow$ downpour" signifies an increasing intensity of rainfall, starting from light (drizzle), progressing to moderate (rain), and culminating in heavy (downpour).
Similarly, "quarrel $\rightarrow$ feud" represents an escalation in the intensity of conflict or disagreement, starting from a relatively minor argument (quarrel) and escalating to a more serious and prolonged dispute (feud).
So, in the analogy, "bicker" would be the appropriate word to fill the blank because it corresponds to the initial, less intense stage of a conflict, much like "drizzle" is the initial, lighter form of rainfall in the rain sequence.