In my case study post, I covered that all events need to be connected by cause and effect for your essay to have unity.
But there are actually other more advanced options. Any of these will maintain unity in your essay.
Key Principle
A good transition should point upward, not downward.
Bad transitions (at the start of a paragraph):
Time: Two weeks later...
Sequence: Next...
Space: Once we landed in New York...
More info: Furthermore...
These context categories all point "downward": they tell you to keep reading down the page because some kind of new info is coming.
Better transitions (at the start of a paragraph):
Cause and effect: Because of this...
Similar or parallel action: In the same way...
Contrast: However...
Premise + Exception: Despite this...
Subversion of expectation: Considering [event], it was surprising that...
Fulfillment of expectation: Just as expected...
These context categories point "upward": they invite the reader to consider how previous information will relate to upcoming information.
A fancy way to say this is that these transitions allow the reader to contextualize upcoming content with respect to previous content. Bonus points if your upcoming content recontextualizes previous content. (That means it makes us see previous content in a new way.)
Side Note
These principles also apply to academic (school) essay writing.