~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
~ひょうしに(~拍子に)   => the moment [A], unintentionally / inadvertently caused something to happen N1
...なり...なり => [A] or [B] or~ N1
Selection
...なりなんなり... => any,anything,whatever N1
Vague
~ふり(~振り)      => to pretend; to act as if N3
通り (とおり/どおり) => in the same way as; in the way; as ~ N2
たり~たり => do such things as A and B N5
限り => to limit... N3
Limit, limit
... ばかり => About … N2
More or less in quantity