Geodesic
Twistors, Kähler manifolds, and bimeromorphic geometry. II
Journal of the American Mathematical Society, Tome 05 (1992) no. 2, pp. 317-325

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Using examples [13] of compact complex $3$-manifolds that arise as twistor spaces, we show that the class of compact complex manifolds bimeromorphic to Kähler manifolds is not stable under small deformations of complex structure. 
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LeBrun, Claude; Poon, Yat Sun. Twistors, Kähler manifolds, and bimeromorphic geometry. II. Journal of the American Mathematical Society, Tome 05 (1992) no. 2, pp. 317-325. doi: 10.1090/S0894-0347-1992-1137099-7

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