Addressing the question in the title, the prefix peri- (“word-forming element meaning "around, about, enclosing”) often is used as a modifier referring to times or things near some event or thing (as in, eg, perinatal (“Of or pertaining to the time around birth”), pericardium, etc).
However, peri- doesn't fit into the main question's context in an obvious way. (Suggestions in other answers, such as Preetie's pre-launch and post-launch and Mario's circum-, seem better suited for the main question than is peri-.) For the example sentence, the current wording with before and after seems likely to be the most concise and suitable arrangement.
Again addressing the question in the title, the terms setup and teardown often are used to denote preparation before an event, and removal of equipment, etc, after it. Terms runup (“A period of time just before an important event”) and buildup also are used.