"Neighbor Rosicky" begins in medias res and proceeds in straight diegetic chronological time until one of the various instances of analepsis occurs, which shifts not only the order of time but the focalization as well. What this means is that Cather's story starts in the middle of the scene (in medias res) in which Dr. Burleigh, who has evidently just examined Anton Rosicky, tells him that his heart is wearing out and that he needs to rest:
It's your heart that makes you short of breath, I tell you. You're sixty-five years old, and you've always worked hard, and your heart's tired.
The chronology progresses in uninterrupted diegetic chronological order until Dr. Burleigh, to whom the focalization has shifted--which makes him the focalizer--introduces analepsis by having a flashback to an incident some time in the past (i.e., earlier in the story) when he stopped for breakfast at the Rosicky farm after a nearby birth in the middle of the night. At the end of the analepsis, Cather returns the focalization to Rosicky who shops a little, then drives his horse and wagon homeward, stopping at "the graveyard, which lay just at the edge of his own hay-land" where he engages in minor prolepsis musings in a minor flashforward to his upcoming time in the graveyard:
A man could lie down in the long grass and see the complete arch of the sky over him, hear the wagons go by; in summer the mowing-machine rattled right up to the wire fence. And it was so near home.
The story again proceeds in diegetic chronological time with periodic recurrence of analepsis, as when Rosicky tells stories of when he lived in big cities: "You boys like me to tell you about some of dem hard times I been through in London?"
The conclusion of the story once again follows the dramatic events in diegetic time, without analepsis or proplepsis, thus adding to the suspense and emotional impact of the ending of Rosicky's life, whose whole life story we have heard and experienced as he relived it.
diegetic: the time-space progression created in any given story.
chronological: occurring in consecutive order in a narrative’s digetic time.
focalization: directing attention to events, accomplished through a character or narrator.
analepsis: leaving diegetic chronological time by narrating an earlier event, flashing back to an earlier event, also called a past event.
prolepsis: leaving diegetic chronological time by narrating an anticipated or future event, flashing forward to an upcoming event, that has not (and may not) actually occurred.
flashback: recalling in the present moment a past, or earlier, event in time.
flashforward: anticipating and envisioning in the present moment a future upcoming event.