I’m re-posting the Paragraph Transitions page so it’s easily available to you as you craft your final essay:

Analytic Transitions

• Explain: make sense of something described just above.
• Build on: introduce the next step in a logical argument.
• Question: raise a doubt or even wholly undercut the prior argument.
• Note an unexpected consequence: this combines elements of the prior two: it builds on, but in a way that causes a tonal shift somewhat like calling into question.
• New angle: for example, you might consider sound after focusing on visuals.
• Zoom in: look at an instance of a trend or pattern noted just above.
• Zoom out: name the pattern which the prior ¶'s topic is an example of.
• Intensify: double down on a claim made just above, with (for example) more telling evidence.
• Give another example: keep this to a minimum. It means that the ¶ fails to take us somewhere new. See if you can't present this new example as intensifying your argument, or offering a new angle on the topic.

Narrative Transitions

• Result: what happened next.
• Cause: what led to the events of the prior ¶
• Lateral shift in space: Meanwhile. back at the ranch..."
• Temporal shift: "Two weeks later, ..."