"Agile" processes still have all these steps, they just repeat them in a loop on a much smaller timescale. This allows for a lot more flexibility, and for feedback from the qualification of the first iteration to go in as input to the analysis stage of the next iteration.
But it's worth noting that we need to spend more time on task management with a shorter development cycle.
In waterfall or scrum or whatever, one development cycle often comes with listing tasks, prioritizing, planning, developing, retrospection, or something similar.
If the cycle is long, we can spend more time on each process.
But if the cycle is short, we rush to complete each process and can't spend enough time understanding each process's meaning.
So I focus more on consuming as many stories as possible.
I never think about the product's goal and how I can contribute to it.
So we have to spend more time teaching the purpose of each process.
Or we end up as a failed agile development.