Everywhere I've worked that did "agile" did it this way. The ending of a sprint is always the start of the next one; teams are always in a sprint. If that part of the process can't be changed or removed then one of the best things to do is decouple the sprint cadence from other events. Eg don't put demo, pointing, planning, and retro on the same day. Try to do pointing mid-sprint, if you know what's coming up, so that you're not cramming it in at the end. Don't release to staging/prod at sprint boundaries, do that mid-sprint. The worst is to clump all the meetings, distractions, and stresses together.