Something to emphasize:
Unless you have two bikes and someone working for you in the pits, then bringing a spare bike and/or wheels is little more than anti-DNF insurance. It's not like a crit, where if you flat you can grab a spare wheel, take your free lap, and hop right back into the race. If you flat or have a mechanical during a cross race, you've pretty much conceded any reasonable placing, but it still is worth finishing out the race to cobble together as many series points as possible.