Bottom Bracket size issues I need to replace my bottom bracket on my giant rapid 3, the BB is a    FSA BB-7420ST - 116mm (68x116mm), but it's hard to found or not available.

My Question is: can I use a BB in 68x115 or 117mm (much more easier to found)? No big problem in perspective?
Yes, you can use the suggested alternate BB cartridge sizes.  

The thread (68mm) has to match precisely, but the width of the axle can vary.  The problem is whether 1mm more or less will affect your chainline on the drive side.  Relatively minor changes can upset the extreme cross chain positions.

So if you're a big-back-cog rider, get the narrower BB, or if you ride a lot on the smaller rear cogs, get the wider BB.