~をかわきりに(~を皮切りに)      => One after another; starting with ~ N1
切る => Give up, stop... N3
Happens next
切る/切れる/切れない => to do something completely to the end/unable to do; too much to finish/complete N3
[切「き」]れない => Can't finish/complete A N3
Potential, Possibility
~かぎりなく ... にちかい => Almost, near, like, almost like N... N1
Limit, limit
うちに => While... N3
どちら => Where N5
Doubt
たちまち  => Immediately, Quickly, Suddenly, In a moment or flash N2
Status
ここ/そこ/あそこ/こちら/そちら/あちら => here / there / over there N5
Spatial relations
うちに => While; Before ~ N2
のうちに => Within... N3
Limit
はもちろん/はもとより => Although A is given/obvious; B N3
List, Examples