We initiate the study of nowhere-zero flow reconfiguration. The natural question is whether any two nowhere-zero $k$-flows of a given graph $G$ are connected by a sequence of nowhere-zero $k$-flows of $G$, such that any two consecutive flows in the sequence differ only on a cycle of $G$. We study this problem in the setting of integer flows and group flows, and prove a number of positive and negative results. * The natural reconfiguration variant of Tutte's 5-flow conjecture, stating that any two nowhere-zero 5-flows in any 2-edge-connected graph are connected, is false in the group and integer cases. * All nowhere-zero $\mathbb{Z}_2^8$-flows of every 2-edge-connected graph are connected and for every sufficiently large abelian group $A$, all nowhere-zero $A$-flows of every 2-edge-connected graph are connected. * The group structure affects the answer, contrary to the existence problem for nowhere-zero flows. * We highlight a duality with recoloring in planar graphs and deduce that any two nowhere-zero 7-flows in a planar graph are connected, among other results. * For every 2-edge-connected graph $G$, there is an integer $k$ such that all nowhere-zero $k$-flows of $G$ are connected.

翻译：我们首次研究无零流重配置问题。自然问题是：给定图 $G$ 的任意两个无零 $k$-流，是否可以通过一系列 $G$ 的无零 $k$-流连接起来，使得序列中任意两个相邻流仅在 $G$ 的某个环路上不同？我们在整数流和群流的框架下研究该问题，并证明一系列正面与负面结果。* 图特5-流猜想的自然重配置变体（即任何2-边连通图中任意两个无零5-流均可连通）在群流和整数流情形下均不成立。* 每个2-边连通图的所有无零 $\mathbb{Z}_2^8$-流均可连通；且对于每个足够大的阿贝尔群 $A$，每个2-边连通图的所有无零 $A$-流均可连通。* 与无零流存在性问题不同，群结构会影响该问题的答案。* 我们揭示了与平面图重着色问题的对偶性，并由此证明（以及其他结果）平面图中任意两个无零7-流均可连通。* 对每个2-边连通图 $G$，存在整数 $k$ 使得 $G$ 的所有无零 $k$-流均可连通。