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parameter, and a small asymmetry for the V$_{a}$ parameter. The right p anel shows the same PDFs, but for the following combinatio ns of the transport parameters: 

V$_{a}$ ←→ √ K$_{0}$ × 3 δ (4 − δ $^{2}$)(4 − δ ) (C.2) These for ms are inspired by the known degeneracies be- tween para meters. For instance, in diffusion models, the secondary to primary ratio is expected to remain un- changed as long as the effective grammage 〈 x 〉 of the model is left unchanged. For pure diffusion, we obtain (Jones et a l. 2001; Maurin et al. 2006) for the grammage 〈 x 〉 = Σ vL / (2 K ) = Σ L/ (2 cK$_{0}$ ( R / 1GV) $^{δ}$), where Σ is the surface de nsity. Apart from the K$_{0}$ − L degeneracy, the parameters K$_{0}$ and δ are correlated. We find that the com- bination K$_{0}$ × 50 δ is appropriate for removing the K$_{0}$ PDF’s tail (see F ig. C.1). The origin of the value 50 is unclear. It may be rela ted to the energy range covered by B/C HEAO- 3 data on which the fits are based. The combination used for V$_{a}$ [Eq. (C.2)] comes directly from the form of the reac- celeration t erm Eq. (5). Reacceleration only plays a role at low energy, so we can take R δ ≈ 1 and end up with the combinatio n presented in Eq. (C.2). The independent ac- ceptance f$_{i}$$_{nd}$ , defined in Paper I as the ratio of the number of indepen dent samples to the total step number, increases from 1/3 t o 1/2 by using the above described parameter combinations for the four parameter model presented in Fig. C.1. 

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A last combination is for the local bubble parameter r$_{h}$ : 

This c omes from the form of Eq. (10), where the flux damp- ing for radioactive species (due to the local bubble) is ef- fective only at low energy ( γ ≈ 1, R ≈ 1). 

## Appendix D: Datasets for CR measurements 

## D.1. B/C ratio 

Unless specified otherwise, the reference B/C dataset used throughout the paper is denoted dataset F: it consists of i) low-energy data taken by the IMP7-8 (Garcia-Munoz et al. 1987), the Voyager 1&2 (Lukasiak et al. 1999), and the ACE-CRIS (de Nolfo et al. 2006) spacecrafts; ii) intermediate energies acquired by HEA0-3 data (Engelmann et al. 1990); and iii) higher energy data from Spacelab (Swordy et al. 1990) and the published CREAM data (Ahn et al. 2008). Other existing data are discarded either because of their too large error bars, or because of their inconsistency with the above data (see Paper I). 

## D.2. Isotopic and elemental ratios of radioactive species 

For $^{10}$Be/$^{9}$Be, the data are taken from balloon flights (Hagen et al. 1977; Buffington et al. 1978; Webber & Kish 1979), including the ISOMAX balloon- borne instrument (Hams et al. 2004), and from the IMP-7/8 (Garcia-Munoz et al. 1977), ISEE-3 (Wiedenbeck & Greiner 1980), Ulysses (Connell 1998), 

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