We investigate broad absorption line (BAL) disappearance and emergence using a 470 BAL-quasar sample over <=0.10-5.25 rest-frame years with at least three spectroscopic epochs for each quasar from the Sloan Digital Sky Survey. We identify 14 disappearing BALs over <=1.73-4.62 rest-frame years and 18 emerging BALs over <=1.46-3.66 rest-frame years associated with the CIV{lambda}{lambda}1548,1550 and/or SiIV{lambda}{lambda}1393,1402 doublets, and report on their variability behaviour. BAL quasars in our data set exhibit disappearing/emerging C IV BALs at a rate of 2.3^+0.9^_-0.7_ and 3.0^+1.0^_-0.8_ per cent, respectively, and the frequency for BAL to non-BAL quasar transitions is 1.7^+0.8^_-0.6_ per cent. We detect four re-emerging BALs over <=3.88 rest-frame years on average and three re-disappearing BALs over <=4.15 rest-frame years on average, the first reported cases of these types. We infer BAL lifetimes along the line of sight to be nominally <=100-1000yr using disappearing CIV BALs in our sample. Interpretations of (re-)emerging and (re-)disappearing BALs reveal evidence that collectively supports both transverse-motion and ionization-change scenarios to explain BAL variations. We constrain a nominal CIV/SiIV BAL-outflow location of <=100pc from the central source and a radial size of >=1x10^-7^pc (0.02au) using the ionization-change scenario, and constrain a nominal outflow location of <=0.5pc and a transverse size of ~0.01pc using the transverse-motion scenario. Our findings are consistent with previous work, and provide evidence in support of BALs tracing compact flow geometries with small filling factors.