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In the start-up process of practical gas turbine applications, the modulation of operating condition, especially the variation of global equivalence ratios (ϕ g l o), could cause the variations of stability regimes. The above process is accompanied by the increase of total air flow rates ( m ̇ a i r) when approaching the stable operation condition, and thus the effect of this parameter should also be considered in the operating condition modulation process. This work presents an experimental investigation into the transitions of thermoacoustic modes and flame dynamics in a centrally-staged swirl combustor over a range of ϕ g l o and m ̇ a i r. The present thermoacoustic system exhibits two transitions of thermoacoustic modes with ϕ g l o variation, showing distinct characteristics of pressure oscillation (p ′) and flame structures. To further explore the detailed variation of p ′ characteristics and its link to flame dynamics during two transitions, a nonlinear dynamic analysis of p ′ including its phase and recurrence plots as well as a proper orthogonal decomposition (POD) study have been conducted. The thermoacoustic network analysis and local Rayleigh index analysis have clarified the mode transition mechanism with varying ϕ g l o and m ̇ a i r. The present results can provide a guideline for quantifying the stability regimes of fuel-flexible combustors during the operating condition modulation processes. • Transitions of thermoacoustic modes and flame dynamics are characterized. • Effects of equivalence ratios and air flow rates on the transitions are examined. • Transient processes during different transitions are observed. • Transient mechanisms of thermoacoustic modes and couplings are elucidated. [ABSTRACT FROM AUTHOR]